Compute Distance To:
 Documents Indexed: 64 Publications since 1988, including 1 Book Reviewing Activity: 221 Reviews Co-Authors: 19 Co-Authors with 27 Joint Publications 570 Co-Co-Authors
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### Co-Authors

 37 single-authored 6 Shestakov, Ivan Pavlovich 4 Klement’ev, S. G. 3 Mishchenko, Sergeĭ Petrovich 3 Subbotin, Igor Yakov 2 Bahturin, Yuri 2 Giambruno, Antonio 2 Mikhalëv, Aleksandr Aleksandrovich 2 Regev, Amitai 2 Smirnov, Alexandr Alexandrovich 1 de Morais Costa, Otto Augusto 1 Dobrynin, Nickolai A. 1 Duchamp, Gerard Henry Edmond 1 La Mattina, Daniela 1 Monteiro Alves, Ilana Z. 1 Passman, Donald Steven 1 Razmyslov, Yuri P. 1 Shishkin, E. O. 1 Zaĭtsev, Mikhail Vladimirovich 1 Zel’manov, Efim Isaakovich
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### Serials

 10 Journal of Algebra 6 Communications in Algebra 3 Israel Journal of Mathematics 3 Journal of Mathematical Sciences (New York) 3 Journal of Lie Theory 2 Discrete Mathematics 2 Mathematical Notes 2 Moscow University Mathematics Bulletin 2 Russian Mathematical Surveys 2 Archiv der Mathematik 2 Proceedings of the American Mathematical Society 2 Siberian Mathematical Journal 2 International Journal of Algebra and Computation 2 Sbornik: Mathematics 1 Matematicheskie Zametki 1 Journal of Pure and Applied Algebra 1 Monatshefte für Mathematik 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 St. Petersburg Mathematical Journal 1 Serdica Mathematical Journal 1 Izvestiya: Mathematics 1 Fundamental’naya i Prikladnaya Matematika 1 Journal of Algebra and its Applications 1 De Gruyter Expositions in Mathematics 1 Groups, Geometry, and Dynamics 1 São Paulo Journal of Mathematical Sciences 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika
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### Fields

 58 Nonassociative rings and algebras (17-XX) 37 Associative rings and algebras (16-XX) 6 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Group theory and generalizations (20-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 1 Commutative algebra (13-XX)

### Citations contained in zbMATH Open

48 Publications have been cited 375 times in 212 Documents Cited by Year
Identities in the enveloping algebras for modular Lie superalgebras. Zbl 0752.17001
1992
Poisson PI algebras. Zbl 1156.17005
Mishchenko, S. P.; Petrogradsky, V. M.; Regev, A.
2007
Growth of finitely generated polynilpotent Lie algebras and groups, generalized partitions, and functions analytic in the unit circle. Zbl 0931.17007
1999
Matrix algebras of polynomial codimension growth. Zbl 1127.16018
Giambruno, A.; La Mattina, D.; Petrogradsky, V. M.
2007
Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions. Zbl 0890.17002
1997
Intermediate growth in Lie algebras and their enveloping algebras. Zbl 0964.17005
1996
Examples of self-iterating Lie algebras. Zbl 1109.17008
2006
Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra. Zbl 0955.17002
Mishchenko, S. P.; Petrogradsky, V. M.
1999
Nil graded self-similar algebras. Zbl 1229.17025
Petrogradsky, Victor M.; Shestakov, Ivan P.; Zelmanov, Efim
2010
On Lie algebras with nonintegral $$q$$-dimensions. Zbl 0873.17014
1997
Wreath products and Kaluzhnin-Krasner embedding for Lie algebras. Zbl 1173.17008
Petrogradsky, V. M.; Razmyslov, Yu. P.; Shishkin, E. O.
2007
Examples of self-iterating Lie algebras. II. Zbl 1253.17011
Petrogradsky, V. M.; Shestakov, I. P.
2009
Polycyclic restricted Lie algebras. Zbl 1054.17014
Passman, D. S.; Petrogradsky, V. M.
2001
Nil Lie $$p$$-algebras of slow growth. Zbl 1430.17055
2017
Witt’s formula for restricted Lie algebras. Zbl 1035.17027
2003
Self-similar associative algebras. Zbl 1293.16020
Petrogradsky, V. M.; Shestakov, I. P.
2013
On properties of the Fibonacci restricted Lie algebra. Zbl 1280.17019
Petrogradsky, V. M.; Shestakov, I. P.
2013
Fractal nil graded Lie superalgebras. Zbl 1405.17055
2016
On some types of intermediate growth in Lie algebras. Zbl 0823.17015
1993
Lie structure of truncated symmetric Poisson algebras. Zbl 1427.17033
Monteiro Alves, Ilana Z.; Petrogradsky, Victor
2017
Codimension growth of strong Lie nilpotent associative algebras. Zbl 1226.16017
2011
Poisson identities of enveloping algebras. Zbl 1214.17008
2006
On types of super exponential growth of identities in Lie PI-algebras. Zbl 0876.17006
1995
On the complexity functions for T-ideals of associative algebras. Zbl 1010.16021
2000
Exponents of subvarieties of upper triangular matrices over arbitrary fields are integral. Zbl 0960.16031
2000
Fractal just infinite nil Lie superalgebra of finite width. Zbl 1422.16019
de Morais Costa, Otto Augusto; Petrogradsky, Victor
2018
Infinite dimensional Lie superalgebras. Zbl 0762.17001
Bakhturin, Yu. A.; Mikhalev, A. A.; Petrogradskiĭ, V. M.; Zaĭtsev, M. V.
1992
Characterization of non-matrix varieties of associative algebras. Zbl 1221.16020
Mishchenko, S. P.; Petrogradsky, V. M.; Regev, A.
2011
Polynomial identities in smash products. Zbl 1014.17006
2002
2000
2000
Exponential Schreier’s formula for free Lie algebras and its applications. Zbl 0983.17007
1999
Growth of subalgebras for restricted Lie algebras and transitive actions. Zbl 1150.17019
2005
On Jordan doubles of slow growth of Lie superalgebras. Zbl 1437.17011
2019
Multiple zeta functions and asymptotic structure of free Abelian groups of finite rank. Zbl 1117.20021
2007
Enumeration of algebras close to absolutely free algebras and binary trees. Zbl 1081.17004
2005
Scale for codimension growth of Lie algebras. Zbl 1011.17004
1998
On the existence of an identity in the restricted envelope. Zbl 0721.17011
1991
Exponential generating functions and complexity of Lie varieties. Zbl 1014.17005
1999
On growth of Lie algebras, generalized partitions, and analytic functions. Zbl 0970.17003
2000
One-sided ideal growth of free associative algebras. Zbl 1110.16017
2006
Growth of solvable Lie superalgebras. Zbl 1126.17012
Klementyev, S. G.; Petrogradsky, V. M.
2005
2002
On generating functions for subalgebras of free Lie superalgebras. Zbl 0992.17003
2002
Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras. Zbl 1470.16041
2021
Nil restricted Lie algebras of oscillating intermediate growth. Zbl 1482.17043
2021
On the numerical characteristics of subvarieties for three varieties of Lie algebras. Zbl 0955.17003
1999
Schreier’s formulae for free Lie algebras, their applications and asymptotics. Zbl 0983.17008
2000
Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras. Zbl 1470.16041
2021
Nil restricted Lie algebras of oscillating intermediate growth. Zbl 1482.17043
2021
On Jordan doubles of slow growth of Lie superalgebras. Zbl 1437.17011
2019
Fractal just infinite nil Lie superalgebra of finite width. Zbl 1422.16019
de Morais Costa, Otto Augusto; Petrogradsky, Victor
2018
Nil Lie $$p$$-algebras of slow growth. Zbl 1430.17055
2017
Lie structure of truncated symmetric Poisson algebras. Zbl 1427.17033
Monteiro Alves, Ilana Z.; Petrogradsky, Victor
2017
Fractal nil graded Lie superalgebras. Zbl 1405.17055
2016
Self-similar associative algebras. Zbl 1293.16020
Petrogradsky, V. M.; Shestakov, I. P.
2013
On properties of the Fibonacci restricted Lie algebra. Zbl 1280.17019
Petrogradsky, V. M.; Shestakov, I. P.
2013
Codimension growth of strong Lie nilpotent associative algebras. Zbl 1226.16017
2011
Characterization of non-matrix varieties of associative algebras. Zbl 1221.16020
Mishchenko, S. P.; Petrogradsky, V. M.; Regev, A.
2011
Nil graded self-similar algebras. Zbl 1229.17025
Petrogradsky, Victor M.; Shestakov, Ivan P.; Zelmanov, Efim
2010
Examples of self-iterating Lie algebras. II. Zbl 1253.17011
Petrogradsky, V. M.; Shestakov, I. P.
2009
Poisson PI algebras. Zbl 1156.17005
Mishchenko, S. P.; Petrogradsky, V. M.; Regev, A.
2007
Matrix algebras of polynomial codimension growth. Zbl 1127.16018
Giambruno, A.; La Mattina, D.; Petrogradsky, V. M.
2007
Wreath products and Kaluzhnin-Krasner embedding for Lie algebras. Zbl 1173.17008
Petrogradsky, V. M.; Razmyslov, Yu. P.; Shishkin, E. O.
2007
Multiple zeta functions and asymptotic structure of free Abelian groups of finite rank. Zbl 1117.20021
2007
Examples of self-iterating Lie algebras. Zbl 1109.17008
2006
Poisson identities of enveloping algebras. Zbl 1214.17008
2006
One-sided ideal growth of free associative algebras. Zbl 1110.16017
2006
Growth of subalgebras for restricted Lie algebras and transitive actions. Zbl 1150.17019
2005
Enumeration of algebras close to absolutely free algebras and binary trees. Zbl 1081.17004
2005
Growth of solvable Lie superalgebras. Zbl 1126.17012
Klementyev, S. G.; Petrogradsky, V. M.
2005
Witt’s formula for restricted Lie algebras. Zbl 1035.17027
2003
Polynomial identities in smash products. Zbl 1014.17006
2002
2002
On generating functions for subalgebras of free Lie superalgebras. Zbl 0992.17003
2002
Polycyclic restricted Lie algebras. Zbl 1054.17014
Passman, D. S.; Petrogradsky, V. M.
2001
On the complexity functions for T-ideals of associative algebras. Zbl 1010.16021
2000
Exponents of subvarieties of upper triangular matrices over arbitrary fields are integral. Zbl 0960.16031
2000
2000
2000
On growth of Lie algebras, generalized partitions, and analytic functions. Zbl 0970.17003
2000
Schreier’s formulae for free Lie algebras, their applications and asymptotics. Zbl 0983.17008
2000
Growth of finitely generated polynilpotent Lie algebras and groups, generalized partitions, and functions analytic in the unit circle. Zbl 0931.17007
1999
Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra. Zbl 0955.17002
Mishchenko, S. P.; Petrogradsky, V. M.
1999
Exponential Schreier’s formula for free Lie algebras and its applications. Zbl 0983.17007
1999
Exponential generating functions and complexity of Lie varieties. Zbl 1014.17005
1999
On the numerical characteristics of subvarieties for three varieties of Lie algebras. Zbl 0955.17003
1999
Scale for codimension growth of Lie algebras. Zbl 1011.17004
1998
Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions. Zbl 0890.17002
1997
On Lie algebras with nonintegral $$q$$-dimensions. Zbl 0873.17014
1997
Intermediate growth in Lie algebras and their enveloping algebras. Zbl 0964.17005
1996
On types of super exponential growth of identities in Lie PI-algebras. Zbl 0876.17006
1995
On some types of intermediate growth in Lie algebras. Zbl 0823.17015
1993
Identities in the enveloping algebras for modular Lie superalgebras. Zbl 0752.17001
1992
Infinite dimensional Lie superalgebras. Zbl 0762.17001
Bakhturin, Yu. A.; Mikhalev, A. A.; Petrogradskiĭ, V. M.; Zaĭtsev, M. V.
1992
On the existence of an identity in the restricted envelope. Zbl 0721.17011
1991
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### Cited by 159 Authors

 28 Petrogradsky, Victor Mikhaylovich 23 Zhang, Yongzheng 18 Zaĭtsev, Mikhail Vladimirovich 16 Giambruno, Antonio 16 Ratseev, Sergej Mikhaijlovich 14 La Mattina, Daniela 12 Mishchenko, Sergeĭ Petrovich 10 Liu, Wende 8 Usefi, Hamid 7 Shestakov, Ivan Pavlovich 6 Chen, Liangyun 6 Siciliano, Salvatore 5 Bahturin, Yuri 5 Riley, David Michael 5 Xu, Xiaoning 5 Zel’manov, Efim Isaakovich 4 Ioppolo, Antonio 4 Regev, Amitai 4 Shu, Bin 4 Vieira, Ana Cristina 4 Wang, Xingting 4 Yao, Yufeng 3 Cherevatenko, Ol’ga Ivanovna 3 Dos Santos, Rafael Bezerra 3 Frolova, Yu. Yu. 3 Hu, Xianguo 3 Koshlukov, Plamen Emilov 3 Kucukoglu, Irem 3 Lu, Jiafeng 3 Mu, Qiang 3 Ol’shanskiĭ, Aleksandr Yur’evich 3 Repovš, Dušan D. 3 Simsek, Yilmaz 3 Smoktunowicz, Agata 2 Alahmadi, Adel N. 2 Alsulami, Hamed Hamdan 2 Bergen, Jeffrey 2 Deryabina, Galina 2 Drensky, Vesselin 2 Egorychev, Georgiǐ Petrovich 2 Jain, Surender Kumar 2 Kanel’-Belov, Alekseĭ Yakovlevich 2 Klement’ev, S. G. 2 Krasilnikov, Alexei N. 2 Mikhalëv, Aleksandr Aleksandrovich 2 Millionshchikov, Dmitriĭ Vladimirovich 2 Mishchenko, S. S. 2 Passman, Donald Steven 2 Pchelintsev, Sergeĭ Valentinovich 2 Ren, Li 2 Riyahi, Zahra 2 Salemkar, Ali Reza 2 Subbotin, Igor Yakov 2 Valenti, Angela 2 Wang, Ying 2 Zhang, Chaowen 2 Zheng, Keli 2 Zima, Eugene V. 1 Aslizadeh, Arezoo 1 Bartholdi, Laurent 1 Bayad, Abdelmejid 1 Bessades, D. C. L. 1 Billig, Yuly 1 Bois, Jean-Marie 1 Bondarenko, Nataliya V. 1 Borisenko, Vladimir V. 1 Bouarroudj, Sofiane 1 Bryant, Roger M. 1 Cedó, Ferran 1 Chen, Yan 1 Chen, Yuqun 1 Costa, W. D. S. 1 Crowley, Diarmuid John 1 Davletshin, Maksim Nikolaevich 1 de Morais Costa, Otto Augusto 1 de Oliveira, Marco A. A. 1 do Nascimento, Thais Silva 1 Dobrynin, Nickolai A. 1 Dong, Yanqin 1 Duchamp, Gerard Henry Edmond 1 Ebonzo, Angelo 1 Ferraz, Raul Antonio 1 Ferry, Steven C. 1 Fulman, Jason E. 1 Futorny, Vyacheslav M. 1 Gao, Xiaocheng 1 Gavarini, Fabio 1 Glizburg, Vita I. 1 Greenfeld, Be’eri 1 Guan, Baoling 1 Guo, Mengtian 1 Gupta, Chander Kanta 1 He, Yinghua 1 Holtkamp, Ralf 1 Hua, Xiuying 1 Janssens, Geoffrey 1 Jespers, Eric 1 Kaĭgorodov, Ivan B. 1 Kaplan, Nathan 1 Koçak, Dilber ...and 59 more Authors
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### Cited in 62 Serials

 35 Journal of Algebra 16 Communications in Algebra 11 Journal of Pure and Applied Algebra 11 Journal of Mathematical Sciences (New York) 9 Israel Journal of Mathematics 7 Proceedings of the American Mathematical Society 7 Transactions of the American Mathematical Society 7 International Journal of Algebra and Computation 5 Advances in Applied Mathematics 5 Algebras and Representation Theory 4 Mathematical Notes 4 Moscow University Mathematics Bulletin 4 Monatshefte für Mathematik 4 Science in China. Series A 4 Algebra Colloquium 3 Advances in Mathematics 3 Algebra and Logic 3 Siberian Mathematical Journal 3 Chinese Annals of Mathematics. Series B 3 Acta Mathematica Sinica. English Series 3 Journal of Algebra and its Applications 3 Frontiers of Mathematics in China 3 Science China. Mathematics 2 Linear and Multilinear Algebra 2 Czechoslovak Mathematical Journal 2 Chinese Science Bulletin 2 Journal of the Australian Mathematical Society 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 São Paulo Journal of Mathematical Sciences 2 Journal of Siberian Federal University. Mathematics & Physics 1 Discrete Mathematics 1 Algebra i Logika 1 Annales de l’Institut Fourier 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Annals of Pure and Applied Logic 1 Forum Mathematicum 1 Applicable Algebra in Engineering, Communication and Computing 1 Russian Mathematics 1 St. Petersburg Mathematical Journal 1 Filomat 1 Sbornik: Mathematics 1 Abstract and Applied Analysis 1 Annals of Combinatorics 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Algebra and Discrete Mathematics 1 Mediterranean Journal of Mathematics 1 Chebyshevskiĭ Sbornik 1 Proceedings of the Steklov Institute of Mathematics 1 Groups, Geometry, and Dynamics 1 European Journal of Pure and Applied Mathematics 1 Electronic Research Announcements in Mathematical Sciences 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Research in Number Theory 1 Prikladnaya Diskretnaya Matematika
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### Cited in 23 Fields

 164 Nonassociative rings and algebras (17-XX) 101 Associative rings and algebras (16-XX) 21 Group theory and generalizations (20-XX) 15 Combinatorics (05-XX) 11 Number theory (11-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Computer science (68-XX) 5 General algebraic systems (08-XX) 4 Commutative algebra (13-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Special functions (33-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 2 Information and communication theory, circuits (94-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX)