- Hacettepe Journal of Mathematics and Statistics
- Vol: 45 Issue: 3
- Classical completely prime submodules
Classical completely prime submodules
Authors : Nico J. Groenewald, David Ssevviiri
Pages : 717-729
View : 12 | Download : 5
Publication Date : 2016-06-01
Article Type : Research
Abstract :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 $\beta_cl^c(M)$ the classical completely prime radical of M, we show that for modules over left Artinian rings R, Rad(M) $\subseteq \beta_cl^c(M)$ and Rad($_R$R) = $\beta_cl^c(_RR)$ .Keywords : Classical completely prime submodules, classical prime submodules, prime submodules, module radicals