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
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
收藏
页码:289 / 304
页数:16
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