摘要
主要对 P.F.Smith提出的两个公开问题进行讨论 ,并且证明了 :( 1 )弱 CS模与 uniform模的直和是弱 CS模 ;( 2 )以 Soc M为闭子模的模 M是弱 CS模当且仅当 M=Soc M M′;( 3)如果 M的任何半单子模都是内射的 ,则弱 CS模的直和项也是弱
This paper discussed P.F.Smith′s two open problems and showed the following results: (1) The direct sum of a weak CS module and uniform module is a weak CS module; (2)If Soc M is a closed submodule of M , then M is a weak CS module if and only if M= Soc MM′ ;(3)If M is a weak CS module and any semi simple submodule of M is injective, then the direct summand of M is a weak CS module.
出处
《浙江师大学报（自然科学版）》
2000年第2期129-132,共4页
Journal of Zhejiang Normal University(Natoral Sciences)
关键词
弱CS模
uniform模
直和性
遗传性
CS module
weak CS module
uniform module
finite uniform dimension
