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NOTES ON NILPOTENCY OF NIL SUBRINGS OF ENDOMORPHISM RINGS OF MODULES

 

作者: Yiqiang Zhou,  

 

期刊: Quaestiones Mathematicae  （Taylor Available online 1996）
卷期: Volume 19, issue 1-2  

页码: 1-5

 

ISSN:1607-3606

 

年代: 1996

 

DOI:10.1080/16073606.1996.9631821

 

出版商: Taylor & Francis Group

 

关键词: 16P70;16S50;16D80;Natural classes of modules;endomorphism rings;chain conditions;nil and nilpotency

 

数据来源: Taylor

 

摘要:

A familyKof rightR-modules is called a natural class ifKis closed under submodules, direct sums, infective hulls, and isomorphic copies. The main result of this note is the following: LetKbe a natural class on Mod-RandMεK. IfMsatisfies a.c.c. (or d.c.c.) on the set of submodules {N⊆M:M/Nε K}, then each nil subring of End(MR) is nilpotent.

 

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