WHEN DO THE DIRECT SUMS OF MODULES INHERIT CERTAIN PROPERTIES?

被引：0

作者：

Lee, Gangyong ^{[1
]}

Rizvi, S. Tariq ^{[2
]}

Roman, Cosmin ^{[2
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Ohio State Univ, Dept Math, Lima, OH 45804 USA

来源：

CONTEMPORARY RING THEORY 2011 | 2012年

关键词：

Direct sums; Rickart modules; Baer modules; (FI-)extending modules; (quasi-) continuous modules; annihilators; idempotents; endomorphism rings; QUASI-BAER RINGS; SUMMAND INTERSECTION PROPERTY; ENDOMORPHISM-RINGS; EXTENDING MODULES; RICKART MODULES; PP RINGS; EXTENSIONS; IDEALS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is of obvious interest to know whether an algebraic property of modules is preserved by direct sums of such modules. In this paper we provide a survey of this question for various classes of modules of interest. The question of inheritance of a property by direct sums of modules has been explored for the classes of (quasi-)injective modules and some of their generalizations as a motivation for further work. In the main part of this paper we provide latest results and developments on this question for the related classes of Baer, quasi-Baer, and Rickart modules. Examples are provided that delimit our results and explain the notions. Some open problems are listed at the end of the paper.

引用

页码：47 / 77

页数：31

共 56 条

[1]

[Anonymous], 1973, Algebra: Rings, modules, and categories

[2]

[Anonymous], 1972, Grundlehren der mathematischen Wissenschaften

[3] Triangular matrix representations [J].