CORETRACTABLE MODULES

被引：33

作者：

Amini, B. ^{[1
]}

Ershad, M. ^{[1
]}

Sharif, H. ^{[1
]}

机构：

[1] Shiraz Univ, Dept Math, Coll Sci, Shiraz 71454, Iran

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2009年 / 86卷 / 03期

关键词：

coretractable module; Kasch ring; perfect ring; semi-Artinian ring; max ring; semi-injective module; RETRACTABLE MODULES; ENDOMORPHISM-RINGS; GOLDIE DIMENSION;

D O I：

10.1017/S1446788708000360

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An R-module M is called coretractable if Hom(R) (M/K, M) not equal 0 for any proper submodule K of M. In this paper we study coretractable modules and their endomorphism rings. It turns out that if all right R-modules are coretractable, then R is a right Kasch and (two-sided) perfect ring. However, the converse holds for commutative rings. Also, for a semi-injective coretractable module M(R) with S = End(R) (M), We show that u.dim((S)S) = corank(M(R)).

引用

页码：289 / 304

页数：16

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