MODULES WHICH ARE INVARIANT UNDER IDEMPOTENTS OF THEIR ENVELOPES

被引：8

作者：

Le Van Thuyet ^{[1
]}

Phan Dan ^{[2
]}

Truong Cong Quynh ^{[3
]}

机构：

[1] Hue Univ, Dept Math, 3 Le Loi, Hue, Vietnam

[2] Banking Univ Ho Chi Minh City, 39 Ham Nghi, Ho Chi Minh City, Vietnam

[3] Danang Univ, Dept Math, 459 Ton Duc Thang, Danang, Vietnam

来源：

COLLOQUIUM MATHEMATICUM | 2016年 / 143卷 / 02期

关键词：

idempotent-invariant module; extending-invariant module; quasi continuous; AUTOMORPHISMS; RINGS;

D O I：

10.4064/cm6496-1-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is X-idempotent-invariant if there exists an X -envelope u : M -> X such that for any idempotent g is an element of End(X) there exists an endomorphism f : M -> M such that uf = gu. The properties of this class of modules are discussed. We prove that M is X-idempotent-invariant if and only if for every decomposition X = circle plus(i is an element of I) Xi, we have M = circle plus(i is an element of I) (u(-1) (X-i) boolean AND M). Moreover, some generalizations of X-idempotent-invariant modules are considered.

引用

页码：237 / 250

页数：14

共 15 条

[1]

ANDERSON F., 1992, Rings and Categories of Modules

[2] Indecomposable flat cotorsion modules [J].