C3-Modules

被引：22

作者：

Amin, Ismail ^{[1
]}

Ibrahim, Yasser ^{[1
]}

Yousif, Mohamed ^{[2
]}

机构：

[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

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

来源：

ALGEBRA COLLOQUIUM | 2015年 / 22卷 / 04期

关键词：

injective and quasi-injective modules; C2-modules and C3-modules; PROJECTIVE MODULES; INJECTIVE MODULES; PERFECT RINGS; REPRESENTATIONS;

D O I：

10.1142/S1005386715000553

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A boolean AND B = 0, then A circle plus B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.

引用

页码：655 / 670

页数：16

共 27 条

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