Classical completely prime submodules

Authors : Nico J GROENEWALD, David SSEVVİİRİ

Pages : 717-729

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Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :We define and characterize classical completely prime submodules which are a generalization of both completely prime ideals in rings and reduced modules insert ignore into journalissuearticles values(as defined by Lee and Zhou in [18]);. A comparison of these submodules with other “prime” submodules in literature is done. If Radinsert ignore into journalissuearticles values(M); is the Jacobson radical of M and $\beta_cl^cinsert ignore into journalissuearticles values(M);$ the classical completely   prime radical of M, we show that for modules over left Artinian rings R, Radinsert ignore into journalissuearticles values(M); $\subseteq \beta_cl^cinsert ignore into journalissuearticles values(M);$  and Radinsert ignore into journalissuearticles values($_R$R); = $\beta_cl^cinsert ignore into journalissuearticles values(_RR);$ .
Keywords : Classical completely prime submodules, classical prime submodules, prime submodules, module radicals