Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups

被引：0

作者：

Blagoveshchenskaya, E. A. ^{[1
]}

Mikhalev, A. V. ^{[2
]}

机构：

[1] Emperior Alexander I St Petersburg State Transport, Emperior Alexander 1St, St Petersburg 190031, Russia

[2] Moscow MV Lomonosov State Univ, Moscow 119991, Russia

来源：

VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2023年 / 56卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

torsion-free abelian groups; endomorphism rings; matrix representations;

D O I：

10.1134/S1063454123030032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Non-isomorphic direct decompositions of torsion-free Abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.

引用

页码：341 / 349

页数：9

共 50 条

[1] Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups
E. A. Blagoveshchenskaya
A. V. Mikhalev
Vestnik St. Petersburg University, Mathematics, 2023, 56 : 341 - 349
[2] REMARKS ON ENDOMORPHISM RINGS OF TORSION-FREE ABELIAN-GROUPS
VANLEEUW.
ACTA SCIENTIARUM MATHEMATICARUM, 1971, 32 (3-4): : 346 - +
[3] ENDOMORPHISM RINGS OF RANK 2 TORSION-FREE ABELIAN GROUPS
PARR, JT
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (07): : 1048 - &
[4] ENDOMORPHISM RINGS OF RANK 2 TORSION-FREE ABELIAN GROUPS
PARR, JT
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1971, 22 (JUL) : 611 - &
[5] TORSION-FREE ABELIAN-GROUPS WITH ISOMORPHIC ENDOMORPHISM RINGS
HAUPTFLEISCH, GJ
ARCHIV DER MATHEMATIK, 1973, 24 (03) : 269 - 273
[6] TORSION-FREE ABELIAN-GROUPS TORSION OVER THEIR ENDOMORPHISM-RINGS
FATICONI, TG
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1994, 50 (02) : 177 - 195
[7] ENDOMORPHISM-RINGS OF SEPARABLE TORSION-FREE ABELIAN-GROUPS
DUGAS, M
GOBEL, R
HOUSTON JOURNAL OF MATHEMATICS, 1985, 11 (04): : 471 - 483
[8] ON TOPOLOGICAL RINGS WHICH ARE ENDOMORPHISM-RINGS OF REDUCED TORSION-FREE ABELIAN-GROUPS
DESTE, G
QUARTERLY JOURNAL OF MATHEMATICS, 1981, 32 (127): : 303 - 311
[9] On the Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Rings and Some Groups of Homomorphisms
Pushkova, T. A.
Sebel'din, A. M.
MATHEMATICAL NOTES, 2017, 101 (3-4) : 688 - 692
[10] On the Question of Definability of Homogeneously Decomposable Torsion-Free Abelian Groups by Their Homomorphism Groups and Endomorphism Rings
Pushkova, T. A.
Sebel'din, A. M.
MATHEMATICAL NOTES, 2020, 108 (1-2) : 117 - 122

← 1 2 3 4 5 →