Classical completely prime submodules

被引：2
|
作者：
Groenewald, Nico J. [1 ]
Ssevviiri, David [2 ]
机构：
[1] Nelson Mandela Metropolitan Univ, Dept Math & Appl Math, POB 77000, Port Elizabeth, South Africa
[2] Makerere Univ, Dept Math, POB 7062, Kampala, Uganda
来源：
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2016年 / 45卷 / 03期
关键词：
Classical completely prime submodules; classical prime submodules; prime submodules; module radicals; MODULES; RINGS;
D O I：
10.15672/HJMS.20164513096
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define and characterize classical completely prime submodules which are a generalization of both completely prime ideals in rings and reduced modules (as defined by Lee and Zhou in [18]). A comparison of these submodules with other "prime" submodules in literature is done. If Rad(M) is the Jacobson radical of M and beta(c)(cl)(M) the classical completely prime radical of M, we show that for modules over left Artinian rings R, Rad(M) subset of beta(c)(cl)(M) and Rad(R-R) = beta(c)(cl)(R-R).
引用
收藏
页码：717 / 729
页数：13
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