ON ADS MODULES AND RINGS

被引：19

作者：

Truong Cong Quynh ^{[1
]}

Kosan, M. Tamer ^{[2
]}

机构：

[1] Danang Univ, Dept Math, Danang City, Vietnam

[2] Gebze Inst Technol, Dept Math, TR-41400 Gebze, Turkey

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 08期

关键词：

ADS module; ADS ring; CS module; Fully-invariant module; 16D50; 16D60; 16D80;

D O I：

10.1080/00927872.2013.788185

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A right module M over a ring R is said to be ADS if for every decomposition M=S circle plus T and every complement T of S, we have M=S circle plus T. In this article, we study and provide several new characterizations of this new class of modules. We prove that M is semisimple if and only if every module in sigma[M] is ADS. SC and SI rings also characterized by the ADS notion. A ring R is right SC-ring if and only if every 2-generated singular R-module is ADS.

引用

页码：3541 / 3551

页数：11

共 12 条

[1] ADS modules [J].

Alahmadi, Adel ;

Jain, S. K. ;

Leroy, Andre .

JOURNAL OF ALGEBRA, 2012, 352 (01) :215-222

[2]

Anderson F. W., 1974, Rings and Categories of Modules

[3]

Dung N. V., 1994, PITMAN RES NOTES MAT, V313

[4]

Fuchs L., 1970, PURE APPL MATH SER M, V36

[5]

Fuchs L., 1970, INFINITE ABELIAN GRO, V1

[6]

Goodearl K. R., 1972, MEMORIES AM MATH SOC, V124

[7]

Koike K., 1995, MATH J OKAYAMA U, V37, P99

[8]

Mohammed S. H., 1990, London Math. Soc. LN, V147

[9]

Nicholson W. K., 2003, CAMB TRACT MATH

[10]

RIZVI ST, 1990, LECT NOTES MATH, V1448, P116

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