×

Jerzy Łoś and a history of Abelian groups in Poland. (English) Zbl 1033.20057

The author describes the development of Abelian group theory in Poland after the Second World War. Especially, the connections of Abelian groups with model theory and ring theory are mentioned.

MSC:

20Kxx Abelian groups
01A60 History of mathematics in the 20th century
20-03 History of group theory

Keywords:

Abelian groups
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] S. Balcerzyk, On algebraically compact groups of I. Kaplansky , Fund. Math. 44 (1957), 91-93. · Zbl 0079.03403
[2] ——–, On factor groups of some subgroups of a complete direct sum of infinite cyclic groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 141-143.
[3] ——–, On classes of abelian groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 9 (1961), 327-329. · Zbl 0100.02804
[4] ——–, The global dimension of the group rings of abelian groups III, Fund. Math. 67 (1970), 241-250. · Zbl 0204.33901
[5] ——–, An introduction to homological algebra , PWN, Warszawa, 1970.
[6] S. Balcerzyk and T. Józefiak, Commutative rings , PWN, Warszawa, 1985. · Zbl 0070.02002
[7] E. Cartan and S., Eilenberg, Homological algebra , Princeton Univ. Press, 1956. · Zbl 0075.24305
[8] C.C. Chang and H.J. Keisler, Model theory , Stud. Logic Found. Math., vol. 73 -1973.
[9] P.J. Cohen, The independence of the continuum hypothesis I, Proc. Nat. Acad. Sci. USA 50 (1963), 1143-1148. · Zbl 0192.04401
[10] ——–, The independence of the continuum hypothesis II, Proc. Nat. Acad. Sci. USA 51 (1964), 105-110.
[11] S. Eilenberg, Singular homology theory , Ann. of Math. 45 (1944), 407-447. JSTOR: · Zbl 0061.40603
[12] S. Eilenberg and S. MacLane, Group extensions and homology , Ann. of Math. 43 (1942), 757-831. JSTOR: · Zbl 0061.40602
[13] ——–, Cohomology theory in abstract groups , I and II, Ann. of Math. 48 (1945), 51-78, 326-341. JSTOR: · Zbl 0029.34001
[14] C. Faith, Algebra II. Ring theory , Springer-Verlag, New York, 1976. · Zbl 0335.16002
[15] L. Fuchs, Infinite abelian groups , Academic Press, New York, 1970. · Zbl 0209.05503
[16] L. Fuchs and E. Sąsiada, Note on orderable groups , Ann. Univ. Sci. Budapest. de Rolando Eötvös Nominatae 7 (1964), 13-17. · Zbl 0192.12902
[17] A. Hulanicki, Algebraic characterization of abelian divisible groups which admit compact topologies , Fund. Math. 44 (1957), 192-197. · Zbl 0082.02604
[18] ——–, Algebraic structure of compact abelian groups which admit compact topologies , Bull. Acad. Polon. Sci., Sér. Sci. Math. 6 (1958), 71-73. · Zbl 0081.26001
[19] ——–, The structure of the factor group of an unrestricted sum of abelian groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 10 (1962), 77-80. · Zbl 0107.26003
[20] N. Jacobson, Structure of rings , American Math. Soc., Providence, RI, 1956. (Russian transl. “Strojenije kolec”, Moskva, 1961)
[21] C.U. Jensen and H. Lenzing, Model theoretic algebra with particular emphasis on fields, rings, modules , Algebra Logic Appl., vol. 2, Gordon & Breach Science Publ., New York, 1989. · Zbl 0728.03026
[22] L. Jeśmanowicz, Caricatures of Polish mathematicians (S. Balcerzyk, B. Kamiński and Z. Leszczyński, eds.), Nicholas Copernicus University, Toruń, 1994.
[23] R. Kiełpiński and D. Simson, On pure homological dimension , Bull. Acad. Polon. Sci., Sér. Sci. Math. 23 (1974), 1-6. · Zbl 0303.16016
[24] M. Król and E. Sąsiada, The complete direct sums of torsion-free abelian groups of rank \(1\) which are separable , Bull. Acad. Polon. Sci., Sér. Sci. Math. 8 (1960), 1-2. · Zbl 0123.02402
[25] J. Łoś, The algebraic treatment of the methodology of elementary deductive systems , Studia Logica 2 (1954), 151-212. · Zbl 0067.25101
[26] ——–, On the categoricity in power of elementary deductive systems and some related problems , Colloq. Math. 3 (1954), 58-62. · Zbl 0055.00505
[27] ——–, Sur le théoréme de Gödel pur les théories indénombrables , Bull. Acad. Polon. Sci., Sér. Sci. Math. 2 (1954), 319-320. · Zbl 0056.01002
[28] ——–, On the extending of models I, Fund. Math. 42 (1955), 38-54. · Zbl 0065.00401
[29] ——–, Quelques remarques, théorémes et problémes sur les classes definissables d’algébres , Stud. Logic Found. Math. (Mathematical Interpretation of Formal Systems), North-Holland Publ. Co., Amsterdam, 1955. · Zbl 0068.24401
[30] ——–, Abelian groups that are direct summands of every abelian group which contains them as pure subgroups , Fund. Math. 44 (1957), 84-90. · Zbl 0079.03402
[31] ——–, Linear equations and pure subgroups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 13-18. · Zbl 0083.25101
[32] ——–, Generalized limits in algebraically compact groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 19-21. · Zbl 0083.25003
[33] J. Łoś, E. Sąsiada and Z. Słomiński, On abelian groups with hereditarily generating systems , Publ. Math. Debrecen 4 (1956), 351-356. · Zbl 0070.25702
[34] S. MacLane, “Samuel Eilenberg,” Notices of the Amer. Math. Soc. 45 (1998), 1344-1352. · Zbl 0908.01023
[35] A. Mostowski and E. Sąsiada, On the bases of modules over a principal ideal ring , Bull. Acad. Polon. Sci., Sér. Sci. Math. 3 (1955), 477-478. · Zbl 0065.26102
[36] B.L. Osofsky, Homological dimensions and the continuum hypothesis , Trans. Amer. Math. Soc. 132 (1968), 217-230. JSTOR: · Zbl 0157.08201
[37] R.S. Pierce, The global dimensions of Boolean rings , J. Algebra 7 (1967), 91-99. · Zbl 0149.28103
[38] E. Sąsiada, On abelian groups every countable subgroup of which is an endomorphic image , Bull. Acad. Polon. Sci., Sér. Sci. Math. 2 (1954), 359-362. · Zbl 0058.01802
[39] ——–, An application of Kulikov’s basic subgroups in the theory of abelian mixed groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 4 (1956), 411-413. · Zbl 0070.25703
[40] ——–, Construction of a directly indecomposable abelian group of a power higher than that of the continuum , Bull. Acad. Polon. Sci., Sér. Sci. Math. 5 (1957), 701-703. · Zbl 0079.03404
[41] ——–, Construction of a directly indecomposable abelian group of a power higher than that of the continuum. II, Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 23-26. · Zbl 0085.01701
[42] ——–, Proof that every countable and reduced torsion-free abelian group is slender , Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 143-144. · Zbl 0085.01702
[43] ——–, On the isomorphism of decompositions of torsion-free abelian groups into complete direct sum of groups of rank one , Bull. Acad. Polon. Sci., Sér. Sci. Math. 7 (1959), 145-149. · Zbl 0085.01703
[44] ——–, On two problems concerning endomorphism groups , Ann. Sci. Budapest. de Rolando Eötvös Nominatae 2 (1959), 65-66. · Zbl 0096.01504
[45] ——–, Negative solution of I. Kaplansky’s first test problem for abelian groups and a problem of K. Borsuk concerning the homology groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 9 (1961), 331-334. · Zbl 0105.25902
[46] ——–, Solution of the problem of existence of simple radical ring , Bull. Acad. Polon. Sci., Sér. Sci. Math. 9 (1961), 257. · Zbl 0102.27501
[47] ——–, Some remarks on the splitting problem for mixed abelian groups , Bull. Acad. Polon. Sci., Sér. Sci. Math. 36 (1988), 383-389. · Zbl 0757.20015
[48] E. Sąsiada and P.M. Cohn, An example of a simple radical ring , J. Algebra 5 (1967), 373-377. · Zbl 0189.03501
[49] E. Sąsiada and A. Suliński, A note on Jacobson radical , Bull. Acad. Polon. Sci., Sér. Sci. Math. 9 (1962), 421-423. · Zbl 0108.26105
[50] D. Simson, On pure global dimension of locally finitely presented Grothendieck categories , Fund. Math. 96 (1977), 91-116. · Zbl 0361.18010
[51] J. Słomiński, The theory of abstract algebras with infinitary operations , Rozprawy Matematyczne 18 (1959), 1-67. · Zbl 0178.34104
[52] ——–, On the determining of the form of congruences in abstract algebras with equationally definable constant elements , Fund. Math. 48 (1960), 325-345. · Zbl 0123.00601
[53] A. Wieczorek, Wspomnienie o Profesorze Jerzym Łosiu (Krótki opis badań i osiągniȩć w dziedzinie matematycznej ekonomii i zastosowań matematyki) , Przegląd Statyst. 45 (1998), 481-486.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.