## Geroldinger, Alfred

Compute Distance To:
 Author ID: geroldinger.alfred Published as: Geroldinger, Alfred; Geroldinger, A. Homepage: http://imsc.uni-graz.at/geroldinger/ External Links: MGP · dblp · GND
 Documents Indexed: 123 Publications since 1987, including 3 Books 3 Contributions as Editor Co-Authors: 58 Co-Authors with 102 Joint Publications 1,250 Co-Co-Authors
all top 5

### Co-Authors

 24 single-authored 19 Gao, Weidong 14 Halter-Koch, Franz 13 Schmid, Wolfgang Alexander 12 Zhong, Qinghai 11 Grynkiewicz, David J. 5 Kainrath, Florian 5 Reinhart, Andreas 4 Chapman, Scott Thomas 4 Hassler, Wolfgang 4 Schneider, Rudolf 3 Fontana, Marco 3 Freeze, Michael 3 Lettl, Günter Hermann Alexander 3 Olberding, Bruce M. 3 Yuan, Pingzhi 2 Baeth, Nicholas R. 2 Blanco, Víctor 2 Elsholtz, Christian 2 Fan, Yushuang 2 Freiman, Gregory A. 2 García Sánchez, Pedro A. 2 Hamidoune, Yahya Ould 2 Kaczorowski, Jerzy 2 Philipp, Andreas 2 Tringali, Salvatore 1 Baginski, Paul 1 Bashir, Aqsa 1 Brantner, Johannes 1 Burkard, Rainer E. 1 Chi, Rui 1 Cziszter, Kálmán 1 Ding, Shuyan 1 Domokos, Mátyás 1 Edel, Yves 1 Facchini, Alberto 1 Foroutan, Andreas 1 Göbel, Rüdiger 1 Gotti, Felix 1 Haase, Gundolf 1 Hegyvári, Norbert 1 Károlyi, Gyula 1 Khadam, Muhammad Azeem 1 Kubertin, Silke 1 Kunisch, Karl 1 Liebmann, Manfred 1 Močkoř, Jiří 1 Nathanson, Melvyn Bernard 1 Oh, Jun-Seok 1 Peichl, Gunther H. 1 Rackham, Laurence 1 Ramacher, Sebastian 1 Ring, Wolfgang 1 Roitman, Moshe 1 Ruzsa, Imre Z. 1 Schaeffer, George J. 1 Schwab, Emil Daniel 1 Smertnig, Daniel 1 Solymosi, József 1 Stadlober, Ernst 1 Stanchescu, Yonutz V. 1 Steinbach, Olaf 1 Wang, Qinghong 1 Woess, Wolfgang
all top 5

### Serials

 8 Journal of Pure and Applied Algebra 6 Journal of Algebra 6 Semigroup Forum 5 Communications in Algebra 5 Acta Arithmetica 5 Journal of Number Theory 4 Colloquium Mathematicum 3 Periodica Mathematica Hungarica 3 European Journal of Combinatorics 3 Journal de Théorie des Nombres de Bordeaux 3 Journal of Algebra and its Applications 2 Houston Journal of Mathematics 2 Rocky Mountain Journal of Mathematics 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Bulletin of the London Mathematical Society 2 Journal of the Korean Mathematical Society 2 Mathematische Zeitschrift 2 Monatshefte für Mathematik 2 Acta Mathematica Hungarica 2 Revista Matemática Iberoamericana 2 Springer Proceedings in Mathematics & Statistics 2 Bollettino dell’Unione Matematica Italiana 1 American Mathematical Monthly 1 Discrete Mathematics 1 Israel Journal of Mathematics 1 Arkiv för Matematik 1 Archiv der Mathematik 1 Ars Combinatoria 1 Canadian Journal of Mathematics 1 Czechoslovak Mathematical Journal 1 Functiones et Approximatio. Commentarii Mathematici 1 Illinois Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Slovaca 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Results in Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Combinatorica 1 Internationale Mathematische Nachrichten 1 Forum Mathematicum 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 International Journal of Algebra and Computation 1 Acta Mathematica Universitatis Comenianae. New Series 1 Expositiones Mathematicae 1 The Australasian Journal of Combinatorics 1 PU.M.A. Pure Mathematics and Applications 1 The New York Journal of Mathematics 1 The Quarterly Journal of Mathematics 1 Integers 1 Journal of the Australian Mathematical Society 1 JP Journal of Algebra, Number Theory and Applications 1 International Journal of Number Theory 1 Pure and Applied Mathematics (Boca Raton) 1 Journal of Combinatorics and Number Theory 1 Journal of Commutative Algebra 1 Moscow Journal of Combinatorics and Number Theory 1 Actes des Rencontres du C.I.R.M. 1 Advanced Courses in Mathematics – CRM Barcelona
all top 5

### Fields

 104 Group theory and generalizations (20-XX) 79 Commutative algebra (13-XX) 74 Number theory (11-XX) 9 Associative rings and algebras (16-XX) 3 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Geometry (51-XX)

### Citations contained in zbMATH Open

117 Publications have been cited 2,046 times in 578 Documents Cited by Year
Non-unique factorizations. Algebraic, combinatorial and analytic theory. Zbl 1113.11002
Geroldinger, Alfred; Halter-Koch, Franz
2006
Zero-sum problems in finite Abelian groups: a survey. Zbl 1122.11013
Gao, Weidong; Geroldinger, Alfred
2006
Additive group theory and non-unique factorizations. Zbl 1221.20045
Geroldinger, Alfred
2009
Non-unique factorizations: a survey. Zbl 1117.13004
Geroldinger, Alfred; Halter-Koch, Franz
2006
Sets of lengths. Zbl 1391.13004
Geroldinger, Alfred
2016
On non-unique factorizations into irreducible elements. (Über nicht-eindeutige Zerlegungen in irreduzible Elemente.) Zbl 0618.12002
Geroldinger, Alfred
1988
Zero-sum problems in finite abelian groups and affine caps. Zbl 1205.11028
Edel, Yves; Elsholtz, Christian; Geroldinger, Alfred; Kubertin, Silke; Rackham, Laurence
2007
On Davenport’s constant. Zbl 0759.20008
Geroldinger, Alfred; Schneider, Rudolf
1992
Combinatorial number theory and additive group theory. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse). Zbl 1177.11005
Geroldinger, Alfred; Ruzsa, Imre Z.
2009
Local tameness of $$v$$-Noetherian monoids. Zbl 1133.20047
Geroldinger, Alfred; Hassler, Wolfgang
2008
On products of $$k$$ atoms. Zbl 1184.20051
Gao, Weidong; Geroldinger, Alfred
2009
On long minimal zero sequences in finite abelian groups. Zbl 0980.11014
Gao, Weidong; Geroldinger, Alfred
1999
Krull domains and monoids, their sets of lengths, and associated combinatorial problems. Zbl 0897.13001
Chapman, Scott; Geroldinger, Alfred
1997
Monoids of modules and arithmetic of direct-sum decompositions. Zbl 1347.16006
Baeth, Nicholas R.; Geroldinger, Alfred
2014
The large Davenport constant. I: Groups with a cyclic, index 2 subgroup. Zbl 1276.20027
Geroldinger, Alfred; Grynkiewicz, David J.
2013
Arithmetic of seminormal weakly Krull monoids and domains. Zbl 1327.13006
Geroldinger, Alfred; Kainrath, Florian; Reinhart, Andreas
2015
Inverse zero-sum problems. III. Zbl 1213.11178
Gao, Weidong; Geroldinger, Alfred; Grynkiewicz, David J.
2010
On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. Zbl 1207.20055
Geroldinger, Alfred; Kainrath, Florian
2010
The interplay of invariant theory with multiplicative ideal theory and with arithmetic combinatorics. Zbl 1349.13014
Cziszter, Kálmán; Domokos, Mátyás; Geroldinger, Alfred
2016
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules. Zbl 1441.20041
Fan, Yushuang; Geroldinger, Alfred; Kainrath, Florian; Tringali, Salvatore
2017
The catenary degree of Krull monoids. I. Zbl 1253.11101
Geroldinger, Alfred; Grynkiewicz, David J.; Schmid, Wolfgang A.
2011
On the arithmetic of Krull monoids with infinite cyclic class group. Zbl 1208.13003
Geroldinger, A.; Grynkiewicz, D. J.; Schaeffer, G. J.; Schmid, W. A.
2010
Arithmetic of Mori domains and monoids. Zbl 1195.13022
Geroldinger, Alfred; Hassler, Wolfgang
2008
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Zbl 1279.20072
Blanco, V.; García-Sánchez, P. A.; Geroldinger, A.
2011
Congruence monoids. Zbl 1057.13003
Geroldinger, Alfred; Halter-Koch, Franz
2004
Zero-sumfree sequences in cyclic groups and some arithmetical application. Zbl 1018.11011
Geroldinger, Alfred; Hamidoune, Yahya Ould
2002
The set of distances in Krull monoids. Zbl 1255.13002
Geroldinger, Alfred; Yuan, Pingzhi
2012
Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic. Zbl 1279.20073
Geroldinger, Alfred
2013
Factorization problems in semigroups. Zbl 0693.20063
Geroldinger, Alfred; Lettl, Günter
1990
Inverse zero-sum problems. Zbl 1188.11052
Gao, Weidong; Geroldinger, Alfred; Schmid, Wolfgang A.
2007
Factorization theory in commutative monoids. Zbl 1442.20037
Geroldinger, Alfred; Zhong, Qinghai
2020
Zero-sum problems with congruence conditions. Zbl 1259.11020
Geroldinger, A.; Grynkiewicz, D. J.; Schmid, W. A.
2011
On $$v$$-Marot Mori rings and C-rings. Zbl 1327.13064
Geroldinger, Alfred; Ramacher, Sebastian; Reinhart, Andreas
2015
Systems of sets of lengths: transfer Krull monoids versus weakly Krull monoids. Zbl 1434.11036
Geroldinger, Alfred; Schmid, Wolfgang A.; Zhong, Qinghai
2017
Systems of sets of lengths. II. Zbl 1036.11054
Gao, W.; Geroldinger, A.
2000
On the Davenport constant and on the structure of extremal zero-sum free sequences. Zbl 1263.11038
Geroldinger, Alfred; Liebmann, Manfred; Philipp, Andreas
2012
The set of minimal distances in Krull monoids. Zbl 1360.20053
Geroldinger, Alfred; Zhong, Qinghai
2016
On the arithmetic of certain not integrally closed noetherian integral domains. Zbl 0723.20038
Geroldinger, Alfred
1991
A realization theorem for sets of lengths in numerical monoids. Zbl 1396.20069
Geroldinger, Alfred; Schmid, Wolfgang Alexander
2018
Arithmetical theory of monoid homomorphisms. Zbl 0805.20057
Geroldinger, Alfred; Halter-Koch, Franz
1994
Unions of sets of lengths. Zbl 1228.20046
Freeze, Michael; Geroldinger, Alfred
2008
A realization theorem for sets of distances. Zbl 1365.13002
Geroldinger, Alfred; Schmid, Wolfgang A.
2017
On the structure of zerofree sequences. Zbl 0968.11016
Gao, Weidong; Geroldinger, Alfred
1998
Realization theorems for semigroups with divisor theory. Zbl 0751.20045
Geroldinger, Alfred; Halter-Koch, Franz
1992
Systems of sets of lengths. (Systeme von Längenmengen.) Zbl 0721.11042
Geroldinger, A.
1990
The cross number of finite abelian groups. II. Zbl 0833.20061
Geroldinger, Alfred; Schneider, Rudolf
1994
On a conjecture of Kleitman and Lemke. Zbl 0781.20017
Geroldinger, Alfred
1993
On the asymptotic behaviour of lengths of factorizations. Zbl 0751.20044
Geroldinger, Alfred; Halter-Koch, Franz
1992
The critical number of finite abelian groups. Zbl 1214.11113
Freeze, Michael; Gao, Weidong; Geroldinger, Alfred
2009
A structure theorem for sets of lengths. Zbl 0926.11082
Geroldinger, Alfred
1998
Multiplicative ideal theory and factorization theory. Commutative and non-commutative perspectives. Selected papers based on the presentations at the meeting ‘Arithmetic and ideal theory of rings and semigroups’, Graz, Austria, September 22–26, 2014. Zbl 1346.13002
2016
The system of sets of lengths in Krull monoids under set addition. Zbl 1417.11007
Geroldinger, Alfred; Schmid, Wolfgang A.
2016
Monotone chains of factorizations in C-monoids. Zbl 1095.20040
Foroutan, Andreas; Geroldinger, Alfred
2005
Zero-sum problems and coverings by proper cosets. Zbl 1026.20032
Gao, Weidong; Geroldinger, Alfred
2003
The catenary degree of Krull monoids. II. Zbl 1373.20074
Geroldinger, Alfred; Zhong, Qinghai
2015
On the arithmetic of Krull monoids with finite Davenport constant. Zbl 1196.20066
Geroldinger, Alfred; Grynkiewicz, David J.
2009
Non-unique factorizations in block semigroups and arithmetical applications. Zbl 0765.11045
Geroldinger, A.; Halter-Koch, F.
1992
A characterization of class groups via sets of lengths. II. Zbl 1410.11121
Geroldinger, Alfred; Zhong, Qinghai
2017
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems. Zbl 1385.16003
Baeth, N. R.; Geroldinger, A.; Grynkiewicz, D. J.; Smertnig, D.
2015
Sets of arithmetical invariants in transfer Krull monoids. Zbl 1472.13002
Geroldinger, Alfred; Zhong, Qinghai
2019
On strongly primary monoids, with a focus on Puiseux monoids. Zbl 1456.13003
Geroldinger, Alfred; Gotti, Felix; Tringali, Salvatore
2021
Non-unique factorizations in orders of global fields. Zbl 0812.11061
Geroldinger, Alfred; Halter-Koch, Franz; Kaczorowski, Jerzy
1995
The monotone catenary degree of monoids of ideals. Zbl 1419.13005
Geroldinger, Alfred; Reinhart, Andreas
2019
Chains of factorizations in weakly Krull domains. Zbl 0874.13001
Geroldinger, Alfred
1997
Chains of factorizations and sets of lengths. Zbl 0882.20039
Geroldinger, Alfred
1997
On the structure and arithmetic of finitely primary monoids. Zbl 0879.20032
Geroldinger, A.
1996
Half-factorial subsets in infinite abelian groups. Zbl 1095.13531
Geroldinger, Alfred; Göbel, Rüdiger
2003
On zero-sum subsequences of restricted size. IV. Zbl 1090.11014
Chi, Rui; Ding, Shuyan; Gao, Weidong; Geroldinger, A.; Schmid, W. A.
2005
Finitary monoids. Zbl 1043.20033
Geroldinger, Alfred; Halter-Koch, Franz; Hassler, Wolfgang; Kainrath, Florian
2003
On the arithmetic of strongly primary monoids. Zbl 1143.20041
Geroldinger, Alfred; Hassler, Wolfgang; Lettl, Günter
2007
Products of two atoms in Krull monoids and arithmetical characterizations of class groups. Zbl 1309.20050
Baginski, Paul; Geroldinger, Alfred; Grynkiewicz, David J.; Philipp, Andreas
2013
Analytic and arithmetic theory of semigroups with divisor theory. Zbl 0780.11046
Geroldinger, Alfred; Kaczorowski, Jerzy
1992
The cross number of finite Abelian groups. Zbl 0814.20033
Geroldinger, Alfred
1994
Long sets of lengths with maximal elasticity. Zbl 1474.13004
Geroldinger, Alfred; Zhong, Qinghai
2018
Half-factorial domains and half-factorial subsets of Abelian groups. Zbl 0994.20046
Gao, Weidong; Geroldinger, Alfred
1998
Quasi-divisor theories and generalizations of Krull domains. Zbl 0853.13012
Geroldinger, Alfred; Močkoř, Jiří
1995
An addition theorem and its arithmetical application. Zbl 1019.11002
Freiman, Gregory; Geroldinger, Alfred
2000
On products of $$k$$ atoms. II. Zbl 1381.20047
Geroldinger, Alfred; Grynkiewicz, David J.; Yuan, Pingzhi
2015
$$T$$-block monoids and their arithmetical applications to certain integral domains. Zbl 0809.13013
Geroldinger, Alfred
1994
The cross number of finite Abelian groups. III. Zbl 0848.20048
Geroldinger, Alfred; Schneider, Rudolf
1996
The catenary degree and tameness of factorizations in weakly Krull domains. Zbl 0897.13002
Geroldinger, Alfred
1997
The set of distances in seminormal weakly Krull monoids. Zbl 1419.11120
Geroldinger, Alfred; Zhong, Qinghai
2016
A characterization of class groups via sets of lengths. Zbl 1447.11011
Geroldinger, Alfred; Schmid, Wolfgang Alexander
2019
The complete integral closure of monoids and domains. II. Zbl 0837.20073
Geroldinger, A.; Halter-Koch, F.; Lettl, G.
1995
On cross numbers of minimal zero sequences. Zbl 0866.11018
Chapman, Scott T.; Geroldinger, Alfred
1996
Transfer principles in the theory of non-unique factorizations. Zbl 1087.13002
Geroldinger, Alfred; Halter-Koch, Franz
2005
The monotone catenary degree of Krull monoids. Zbl 1278.20079
Geroldinger, Alfred; Yuan, Pingzhi
2013
Local and global tameness in Krull monoids. Zbl 1320.20057
Gao, Weidong; Geroldinger, Alfred; Schmid, Wolfgang A.
2015
Sets of lengths in atomic unit-cancellative finitely presented monoids. Zbl 1441.20040
Geroldinger, Alfred; Schwab, Emil Daniel
2018
Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern. (A quantitative result on factorizations of different length in algebraic number fields). Zbl 0721.11041
Geroldinger, Alfred
1990
On the order of elements in long minimal zero-sum sequences. Zbl 1017.20043
Gao, Weidong; Geroldinger, Alfred
2002
On zero-sum sequences in $$\mathbb Z/n \mathbb Z \oplus \mathbb Z/n \mathbb Z$$. Zbl 1078.11010
Gao, Weidong; Geroldinger, Alfred
2003
On the number of subsequences with given sum of sequences over finite abelian $$p$$-groups. Zbl 1141.11013
Gao, Weidong; Geroldinger, Alfred
2007
The complete integral closure of monoids and domains. Zbl 0805.20055
Geroldinger, Alfred
1993
Arithmetical characterizations of divisor class groups. Zbl 0703.20059
Geroldinger, Alfred
1990
Factorization of natural numbers in algebraic number fields. Zbl 0729.11054
Geroldinger, A.
1991
Minimal relations and catenary degrees in Krull monoids. Zbl 1409.13004
Fan, Yushuang; Geroldinger, Alfred
2019
On strongly primary monoids and domains. Zbl 1452.13002
Geroldinger, Alfred; Roitman, Moshe
2020
A characterization of length-factorial Krull monoids. Zbl 1484.13044
Geroldinger, Alfred; Zhong, Qinghai
2021
On minimal zero sequences with large cross number. Zbl 0933.05150
Geroldinger, Alfred; Schneider, Rudolf
1997
On product-one sequences over dihedral groups. Zbl 07495944
Geroldinger, Alfred; Grynkiewicz, David J.; Oh, Jun Seok; Zhong, Qinghai
2022
On strongly primary monoids, with a focus on Puiseux monoids. Zbl 1456.13003
Geroldinger, Alfred; Gotti, Felix; Tringali, Salvatore
2021
A characterization of length-factorial Krull monoids. Zbl 1484.13044
Geroldinger, Alfred; Zhong, Qinghai
2021
On the arithmetic of stable domains. Zbl 1476.13007
Bashir, Aqsa; Geroldinger, Alfred; Reinhart, Andreas
2021
A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions. Zbl 1455.13002
Geroldinger, Alfred; Schmid, Wolfgang Alexander
2021
Factorization theory in commutative monoids. Zbl 1442.20037
Geroldinger, Alfred; Zhong, Qinghai
2020
On strongly primary monoids and domains. Zbl 1452.13002
Geroldinger, Alfred; Roitman, Moshe
2020
Sets of arithmetical invariants in transfer Krull monoids. Zbl 1472.13002
Geroldinger, Alfred; Zhong, Qinghai
2019
The monotone catenary degree of monoids of ideals. Zbl 1419.13005
Geroldinger, Alfred; Reinhart, Andreas
2019
A characterization of class groups via sets of lengths. Zbl 1447.11011
Geroldinger, Alfred; Schmid, Wolfgang Alexander
2019
Minimal relations and catenary degrees in Krull monoids. Zbl 1409.13004
Fan, Yushuang; Geroldinger, Alfred
2019
A characterization of seminormal C-monoids. Zbl 1458.13004
Geroldinger, Alfred; Zhong, Qinghai
2019
A realization theorem for sets of lengths in numerical monoids. Zbl 1396.20069
Geroldinger, Alfred; Schmid, Wolfgang Alexander
2018
Long sets of lengths with maximal elasticity. Zbl 1474.13004
Geroldinger, Alfred; Zhong, Qinghai
2018
Sets of lengths in atomic unit-cancellative finitely presented monoids. Zbl 1441.20040
Geroldinger, Alfred; Schwab, Emil Daniel
2018
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules. Zbl 1441.20041
Fan, Yushuang; Geroldinger, Alfred; Kainrath, Florian; Tringali, Salvatore
2017
Systems of sets of lengths: transfer Krull monoids versus weakly Krull monoids. Zbl 1434.11036
Geroldinger, Alfred; Schmid, Wolfgang A.; Zhong, Qinghai
2017
A realization theorem for sets of distances. Zbl 1365.13002
Geroldinger, Alfred; Schmid, Wolfgang A.
2017
A characterization of class groups via sets of lengths. II. Zbl 1410.11121
Geroldinger, Alfred; Zhong, Qinghai
2017
Sets of lengths. Zbl 1391.13004
Geroldinger, Alfred
2016
The interplay of invariant theory with multiplicative ideal theory and with arithmetic combinatorics. Zbl 1349.13014
Cziszter, Kálmán; Domokos, Mátyás; Geroldinger, Alfred
2016
The set of minimal distances in Krull monoids. Zbl 1360.20053
Geroldinger, Alfred; Zhong, Qinghai
2016
Multiplicative ideal theory and factorization theory. Commutative and non-commutative perspectives. Selected papers based on the presentations at the meeting ‘Arithmetic and ideal theory of rings and semigroups’, Graz, Austria, September 22–26, 2014. Zbl 1346.13002
2016
The system of sets of lengths in Krull monoids under set addition. Zbl 1417.11007
Geroldinger, Alfred; Schmid, Wolfgang A.
2016
The set of distances in seminormal weakly Krull monoids. Zbl 1419.11120
Geroldinger, Alfred; Zhong, Qinghai
2016
Arithmetic of seminormal weakly Krull monoids and domains. Zbl 1327.13006
Geroldinger, Alfred; Kainrath, Florian; Reinhart, Andreas
2015
On $$v$$-Marot Mori rings and C-rings. Zbl 1327.13064
Geroldinger, Alfred; Ramacher, Sebastian; Reinhart, Andreas
2015
The catenary degree of Krull monoids. II. Zbl 1373.20074
Geroldinger, Alfred; Zhong, Qinghai
2015
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems. Zbl 1385.16003
Baeth, N. R.; Geroldinger, A.; Grynkiewicz, D. J.; Smertnig, D.
2015
On products of $$k$$ atoms. II. Zbl 1381.20047
Geroldinger, Alfred; Grynkiewicz, David J.; Yuan, Pingzhi
2015
Local and global tameness in Krull monoids. Zbl 1320.20057
Gao, Weidong; Geroldinger, Alfred; Schmid, Wolfgang A.
2015
Corrigendum to: “The critical number of finite abelian groups”. Zbl 1393.11065
Freeze, Michael; Gao, Weidong; Geroldinger, Alfred
2015
Monoids of modules and arithmetic of direct-sum decompositions. Zbl 1347.16006
Baeth, Nicholas R.; Geroldinger, Alfred
2014
The large Davenport constant. I: Groups with a cyclic, index 2 subgroup. Zbl 1276.20027
Geroldinger, Alfred; Grynkiewicz, David J.
2013
Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic. Zbl 1279.20073
Geroldinger, Alfred
2013
Products of two atoms in Krull monoids and arithmetical characterizations of class groups. Zbl 1309.20050
Baginski, Paul; Geroldinger, Alfred; Grynkiewicz, David J.; Philipp, Andreas
2013
The monotone catenary degree of Krull monoids. Zbl 1278.20079
Geroldinger, Alfred; Yuan, Pingzhi
2013
The set of distances in Krull monoids. Zbl 1255.13002
Geroldinger, Alfred; Yuan, Pingzhi
2012
On the Davenport constant and on the structure of extremal zero-sum free sequences. Zbl 1263.11038
Geroldinger, Alfred; Liebmann, Manfred; Philipp, Andreas
2012
The catenary degree of Krull monoids. I. Zbl 1253.11101
Geroldinger, Alfred; Grynkiewicz, David J.; Schmid, Wolfgang A.
2011
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Zbl 1279.20072
Blanco, V.; García-Sánchez, P. A.; Geroldinger, A.
2011
Zero-sum problems with congruence conditions. Zbl 1259.11020
Geroldinger, A.; Grynkiewicz, D. J.; Schmid, W. A.
2011
A quantitative aspect of non-unique factorizations: the Narkiewicz constants. Zbl 1230.20023
Gao, Weidong; Geroldinger, Alfred; Wang, Qinghong
2011
Inverse zero-sum problems. III. Zbl 1213.11178
Gao, Weidong; Geroldinger, Alfred; Grynkiewicz, David J.
2010
On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. Zbl 1207.20055
Geroldinger, Alfred; Kainrath, Florian
2010
On the arithmetic of Krull monoids with infinite cyclic class group. Zbl 1208.13003
Geroldinger, A.; Grynkiewicz, D. J.; Schaeffer, G. J.; Schmid, W. A.
2010
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Zbl 1474.20117
Blanco, Víctor; García-Sánchez, Pedro A.; Geroldinger, Alfred
2010
Additive group theory and non-unique factorizations. Zbl 1221.20045
Geroldinger, Alfred
2009
Combinatorial number theory and additive group theory. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse). Zbl 1177.11005
Geroldinger, Alfred; Ruzsa, Imre Z.
2009
On products of $$k$$ atoms. Zbl 1184.20051
Gao, Weidong; Geroldinger, Alfred
2009
The critical number of finite abelian groups. Zbl 1214.11113
Freeze, Michael; Gao, Weidong; Geroldinger, Alfred
2009
On the arithmetic of Krull monoids with finite Davenport constant. Zbl 1196.20066
Geroldinger, Alfred; Grynkiewicz, David J.
2009
Group algebras of finite abelian groups and their applications to combinatorial problems. Zbl 1200.05254
Gao, Weidong; Geroldinger, Alfred; Halter-Koch, Franz
2009
On the structure of minimal zero-sum sequences with maximal cross number. Zbl 1263.11093
Geroldinger, Alfred; Grynkiewicz, David J.
2009
Local tameness of $$v$$-Noetherian monoids. Zbl 1133.20047
Geroldinger, Alfred; Hassler, Wolfgang
2008
Arithmetic of Mori domains and monoids. Zbl 1195.13022
Geroldinger, Alfred; Hassler, Wolfgang
2008
Unions of sets of lengths. Zbl 1228.20046
Freeze, Michael; Geroldinger, Alfred
2008
Zero-sum problems in finite abelian groups and affine caps. Zbl 1205.11028
Edel, Yves; Elsholtz, Christian; Geroldinger, Alfred; Kubertin, Silke; Rackham, Laurence
2007
Inverse zero-sum problems. Zbl 1188.11052
Gao, Weidong; Geroldinger, Alfred; Schmid, Wolfgang A.
2007
On the arithmetic of strongly primary monoids. Zbl 1143.20041
Geroldinger, Alfred; Hassler, Wolfgang; Lettl, Günter
2007
On the number of subsequences with given sum of sequences over finite abelian $$p$$-groups. Zbl 1141.11013
Gao, Weidong; Geroldinger, Alfred
2007
Non-unique factorizations. Algebraic, combinatorial and analytic theory. Zbl 1113.11002
Geroldinger, Alfred; Halter-Koch, Franz
2006
Zero-sum problems in finite Abelian groups: a survey. Zbl 1122.11013
Gao, Weidong; Geroldinger, Alfred
2006
Non-unique factorizations: a survey. Zbl 1117.13004
Geroldinger, Alfred; Halter-Koch, Franz
2006
Monotone chains of factorizations in C-monoids. Zbl 1095.20040
Foroutan, Andreas; Geroldinger, Alfred
2005
On zero-sum subsequences of restricted size. IV. Zbl 1090.11014
Chi, Rui; Ding, Shuyan; Gao, Weidong; Geroldinger, A.; Schmid, W. A.
2005
Transfer principles in the theory of non-unique factorizations. Zbl 1087.13002
Geroldinger, Alfred; Halter-Koch, Franz
2005
On a property of minimal zero-sum sequences and restricted sumsets. Zbl 1122.11012
Gao, Weidong; Geroldinger, Alfred
2005
Congruence monoids. Zbl 1057.13003
Geroldinger, Alfred; Halter-Koch, Franz
2004
Zero-sum problems and coverings by proper cosets. Zbl 1026.20032
Gao, Weidong; Geroldinger, Alfred
2003
Half-factorial subsets in infinite abelian groups. Zbl 1095.13531
Geroldinger, Alfred; Göbel, Rüdiger
2003
Finitary monoids. Zbl 1043.20033
Geroldinger, Alfred; Halter-Koch, Franz; Hassler, Wolfgang; Kainrath, Florian
2003
On zero-sum sequences in $$\mathbb Z/n \mathbb Z \oplus \mathbb Z/n \mathbb Z$$. Zbl 1078.11010
Gao, Weidong; Geroldinger, Alfred
2003
Zero-sumfree sequences in cyclic groups and some arithmetical application. Zbl 1018.11011
Geroldinger, Alfred; Hamidoune, Yahya Ould
2002
On the order of elements in long minimal zero-sum sequences. Zbl 1017.20043
Gao, Weidong; Geroldinger, Alfred
2002
Tamely generated ideals in finitary monoids. Zbl 1066.20059
Geroldinger, Alfred; Halter-Koch, Franz
2002
Systems of sets of lengths. II. Zbl 1036.11054
Gao, W.; Geroldinger, A.
2000
An addition theorem and its arithmetical application. Zbl 1019.11002
Freiman, Gregory; Geroldinger, Alfred
2000
On long minimal zero sequences in finite abelian groups. Zbl 0980.11014
Gao, Weidong; Geroldinger, Alfred
1999
On the structure of zerofree sequences. Zbl 0968.11016
Gao, Weidong; Geroldinger, Alfred
1998
A structure theorem for sets of lengths. Zbl 0926.11082
Geroldinger, Alfred
1998
Half-factorial domains and half-factorial subsets of Abelian groups. Zbl 0994.20046
Gao, Weidong; Geroldinger, Alfred
1998
Krull domains and monoids, their sets of lengths, and associated combinatorial problems. Zbl 0897.13001
Chapman, Scott; Geroldinger, Alfred
1997
Chains of factorizations in weakly Krull domains. Zbl 0874.13001
Geroldinger, Alfred
1997
Chains of factorizations and sets of lengths. Zbl 0882.20039
Geroldinger, Alfred
1997
The catenary degree and tameness of factorizations in weakly Krull domains. Zbl 0897.13002
Geroldinger, Alfred
1997
On minimal zero sequences with large cross number. Zbl 0933.05150
Geroldinger, Alfred; Schneider, Rudolf
1997
Chains of factorizations in orders of global fields. Zbl 0874.11073
Geroldinger, Alfred
1997
On the structure and arithmetic of finitely primary monoids. Zbl 0879.20032
Geroldinger, A.
1996
The cross number of finite Abelian groups. III. Zbl 0848.20048
Geroldinger, Alfred; Schneider, Rudolf
1996
On cross numbers of minimal zero sequences. Zbl 0866.11018
Chapman, Scott T.; Geroldinger, Alfred
1996
On quasi divisor theories and systems of valuations. Zbl 0846.13002
Geroldinger, Alfred; Halter-Koch, Franz
1996
Non-unique factorizations in orders of global fields. Zbl 0812.11061
Geroldinger, Alfred; Halter-Koch, Franz; Kaczorowski, Jerzy
1995
Quasi-divisor theories and generalizations of Krull domains. Zbl 0853.13012
Geroldinger, Alfred; Močkoř, Jiří
1995
The complete integral closure of monoids and domains. II. Zbl 0837.20073
Geroldinger, A.; Halter-Koch, F.; Lettl, G.
1995
Arithmetical theory of monoid homomorphisms. Zbl 0805.20057
Geroldinger, Alfred; Halter-Koch, Franz
1994
The cross number of finite abelian groups. II. Zbl 0833.20061
Geroldinger, Alfred; Schneider, Rudolf
1994
The cross number of finite Abelian groups. Zbl 0814.20033
Geroldinger, Alfred
1994
$$T$$-block monoids and their arithmetical applications to certain integral domains. Zbl 0809.13013
Geroldinger, Alfred
1994
On a conjecture of Kleitman and Lemke. Zbl 0781.20017
Geroldinger, Alfred
1993
...and 17 more Documents
all top 5

### Cited by 436 Authors

 73 Geroldinger, Alfred 45 Chapman, Scott Thomas 41 Gao, Weidong 35 Schmid, Wolfgang Alexander 24 Zhong, Qinghai 22 Grynkiewicz, David J. 21 O’Neill, Christopher 20 García Sánchez, Pedro A. 20 Li, Yuanlin 19 Baeth, Nicholas R. 19 Gotti, Felix 18 Halter-Koch, Franz 16 Peng, Jiangtao 15 Smith, William W. 13 Yuan, Pingzhi 13 Zeng, Xiangneng 12 Ordaz, Oscar 12 Qu, Yongke 11 Han, Dongchun 11 Ponomarenko, Vadim 10 Anderson, David Fenimore 9 Domokos, Mátyás 9 Girard, Benjamin 9 Reinhart, Andreas 9 Wang, Guoqing 8 Anderson, Daniel D. 8 Cziszter, Kálmán 8 Hassler, Wolfgang 8 Philipp, Andreas 8 Smertnig, Daniel 8 Tringali, Salvatore 8 Zhang, Hanbin 7 Adhikari, Sukumar Das 7 Fan, Yushuang 7 García García, Juan Ignacio 7 Hui, Wanzhen 7 Liu, Chao 7 Marchan, Luz Elimar 7 Plagne, Alain 7 Rosales, José Carlos 6 Gotti, Marly 6 Kainrath, Florian 6 Llena, David 6 Močkoř, Jiří 6 Oh, Jun-Seok 6 Pelayo, Roberto Carlos 5 Baginski, Paul 5 Coykendall, James 5 Deng, Guixin 5 Frisch, Sophie 5 Hamidoune, Yahya Ould 5 Radziejewski, Maciej 5 Thangadurai, Ravindranathan 4 Blanco, Víctor 4 Chintamani, Mohan N. 4 Freeze, Michael 4 Hong, Siao 4 Juett, Jason Robert 4 Kaczorowski, Jerzy 4 Kaplan, Nathan 4 Li, Xue 4 Moreno-Frías, Maria Angeles 4 Moriya, B. K. 4 Nakato, Sarah 4 Polo, Harold 4 Schaeffer, George J. 4 Yin, Qiuyu 4 Zhao, Pingping 4 Zhuang, Jujuan 3 Balandraud, Éric 3 Brochero Martínez, Fabio Enrique 3 Facchini, Alberto 3 Garcia, Stephan Ramon 3 Ge, Fan 3 Griffiths, Simon 3 He, Xiaoyu 3 Huang, Meiling 3 Kontolatou, Angeliki 3 Lettl, Günter Hermann Alexander 3 Mazumdar, Eshita 3 Okniński, Jan 3 Paul, Prabal 3 Ribas, Sávio 3 Rissner, Roswitha 3 Roy, Bidisha 3 Sarkar, Subha 3 Sissokho, Papa Amar 3 Sun, Fang 3 Sun, Zhi-Wei 3 Wang, Linlin 3 Wang, Qinghong 3 Wiegand, Roger Allen 3 Windisch, Daniel 3 Xia, Limeng 2 Angermüller, Gerhard 2 Ardila, Rene 2 Bachman, Dale 2 Barron, Thomas 2 Bashir, Aqsa 2 Berger, Aaron ...and 336 more Authors
all top 5

### Cited in 108 Serials

 39 Communications in Algebra 36 Journal of Algebra 35 Journal of Number Theory 29 Semigroup Forum 28 Journal of Pure and Applied Algebra 27 International Journal of Number Theory 25 Discrete Mathematics 24 Journal of Combinatorial Theory. Series A 18 Journal of Algebra and its Applications 16 European Journal of Combinatorics 14 Israel Journal of Mathematics 14 Integers 11 Acta Arithmetica 11 Journal of Commutative Algebra 10 Archiv der Mathematik 9 Journal de Théorie des Nombres de Bordeaux 8 Monatshefte für Mathematik 8 International Journal of Algebra and Computation 8 Linear Algebra and its Applications 6 American Mathematical Monthly 6 Rocky Mountain Journal of Mathematics 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Colloquium Mathematicum 5 Czechoslovak Mathematical Journal 5 Mathematica Slovaca 5 Proceedings of the American Mathematical Society 5 Results in Mathematics 5 Forum Mathematicum 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 The Electronic Journal of Combinatorics 4 Periodica Mathematica Hungarica 4 Transactions of the American Mathematical Society 4 The Ramanujan Journal 4 Journal of the Australian Mathematical Society 4 Bollettino dell’Unione Matematica Italiana 4 AIMS Mathematics 3 Advances in Mathematics 3 Functiones et Approximatio. Commentarii Mathematici 3 Manuscripta Mathematica 3 Mathematische Annalen 3 Acta Mathematica Hungarica 3 Designs, Codes and Cryptography 3 Algebras and Representation Theory 3 Communications of the Korean Mathematical Society 3 JP Journal of Algebra, Number Theory and Applications 3 Actes des Rencontres du C.I.R.M. 2 Bulletin of the Australian Mathematical Society 2 Mathematics of Computation 2 Mathematische Zeitschrift 2 Advances in Applied Mathematics 2 Journal of Symbolic Computation 2 Revista Matemática Iberoamericana 2 SIAM Journal on Discrete Mathematics 2 Elemente der Mathematik 2 Expositiones Mathematicae 2 Combinatorics, Probability and Computing 2 The New York Journal of Mathematics 2 Acta Mathematica et Informatica Universitatis Ostraviensis 2 International Electronic Journal of Algebra (IEJA) 2 Arabian Journal of Mathematics 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Information Processing Letters 1 Journal of Mathematical Analysis and Applications 1 Ukrainian Mathematical Journal 1 Arkiv för Matematik 1 Algebra Universalis 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Canadian Journal of Mathematics 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Graph Theory 1 Journal of the Korean Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Ricerche di Matematica 1 Combinatorica 1 Graphs and Combinatorics 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 MSCS. Mathematical Structures in Computer Science 1 Acta Mathematica Universitatis Comenianae. New Series 1 Aequationes Mathematicae 1 European Journal of Operational Research 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Programming. Series A. Series B 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 Annales Mathématiques Blaise Pascal 1 Turkish Journal of Mathematics 1 Finite Fields and their Applications 1 Selecta Mathematica. New Series 1 The Journal of Fourier Analysis and Applications 1 Transformation Groups 1 Central European Journal of Mathematics 1 Algebra and Discrete Mathematics 1 Frontiers of Mathematics in China 1 Optimization Letters 1 Acta Mathematica Universitatis Ostraviensis 1 The College Mathematics Journal ...and 8 more Serials
all top 5

### Cited in 27 Fields

 357 Group theory and generalizations (20-XX) 356 Number theory (11-XX) 211 Commutative algebra (13-XX) 52 Combinatorics (05-XX) 41 Associative rings and algebras (16-XX) 16 Order, lattices, ordered algebraic structures (06-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 10 Computer science (68-XX) 7 Algebraic geometry (14-XX) 7 Convex and discrete geometry (52-XX) 5 $$K$$-theory (19-XX) 5 Information and communication theory, circuits (94-XX) 4 Functional analysis (46-XX) 3 Geometry (51-XX) 3 Operations research, mathematical programming (90-XX) 2 Topological groups, Lie groups (22-XX) 2 Sequences, series, summability (40-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX)