Perfect rings for which the converse of Schur's lemma holds

被引：13

作者：

Haily, A ^{[1
]}

Alaoui, M ^{[1
]}

机构：

[1] Fac Sci, Dept Math, El Jadida, Morocco

来源：

PUBLICACIONS MATEMATIQUES | 2001年 / 45卷 / 01期

关键词：

Schur's lemma; perfect rings; simple module; uniform module;

D O I：

10.5565/PUBLMAT_45101_10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true? and we show that these rings are exactly the primary decomposable ones.

引用

页码：219 / 222

页数：4