Abelian groups as UA-modules over their endomorphism ring

被引：0

作者：

Chistyakov, D. S. ^{[1
]}

机构：

[1] Nizhnii Novgorod State Univ, Nizhnii Novgorod, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 91卷 / 5-6期

关键词：

unique addition module; Abelian group; torsion-free group; quasidecomposition of a group; distributive module; irreducible module; uniserial module; endomorphism ring;

D O I：

10.1134/S0001434612050355

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that V is a module over a ring R. Themodule V is called a unique addition module (UA-module) if it is not possible to change the addition on the set V without changing the action of R on V. In this paper, we find Abelian groups that are UA-modules over their endomorphism ring.

引用

页码：878 / 884

页数：7

共 50 条

[41] MODULES OVER ENDOMORPHISM RING OF A FINITELY GENERATED PROJECTIVE MODULE
SANDOMIERSKI, FL
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 31 (01) : 27 - +
[42] Some mixed abelian groups as modules over the ring of pseudo-rational numbers
Fomin, AA
ABELIAN GROUPS AND MODULES, 1999, : 87 - 100
[43] Isomorphism of a ring to the endomorphism ring of an abelian group
Misyakov V.M.
Journal of Mathematical Sciences, 2005, 128 (6) : 3484 - 3486
[44] THE STABILITY CLASSIFICATION FOR ABELIAN-BY-FINITE GROUPS AND MODULES OVER A GROUP-RING
MARCJA, A
PREST, M
TOFFALORI, C
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1993, 47 : 212 - 226
[45] On Noetherian modules over minimax Abelian groups
Tushev A.V.
Ukrainian Mathematical Journal, 2002, 54 (7) : 1169 - 1180
[46] Computing the endomorphism ring of an ordinary abelian surface over a finite field
Springer, Caleb
JOURNAL OF NUMBER THEORY, 2019, 202 : 430 - 457
[47] Determinability of periodic Abelian groups by their endomorphism groups
Grinshpon, SY
Sebeldin, AM
MATHEMATICAL NOTES, 1995, 57 (5-6) : 457 - 462
[48] ABELIAN-GROUPS QUASI-INJECTIVE OVER THEIR ENDOMORPHISM RINGS
POOLE, GD
REID, JD
CANADIAN JOURNAL OF MATHEMATICS, 1972, 24 (04): : 617 - &
[49] On a property of the endomorphism ring of an abelian group
Misyakov, V. M.
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2010, (11): : 38 - 46
[50] ENDOMORPHISM RING OF POINTED SEPARABLE TORSION-FREE ABELIAN-GROUPS
WEBB, MC
JOURNAL OF ALGEBRA, 1978, 55 (02) : 446 - 454

← 1 2 3 4 5 →