Classical completely prime submodules

Year 2016, Volume: 45 Issue: 3, 717 - 729, 01.06.2016

Nico J. Groenewald David Ssevviiri

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

References

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