[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160075

ON 𝜙-SEMIPRIME SUBMODULES

Ebrahimpour, Mahdieh (Department of Mathematics Vali-e-Asr University)
Mirzaee, Fatemeh (Department of pure Mathematics Shahid Bahonar University)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1099-1108 More about this Journal

Abstract

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let S(M) be the set of all submodules of M and ${\phi}:S(M){\rightarrow}S(M){\cup}\{{\emptyset}\}$ be a function. We say that a proper submodule P of M is a ${\phi}$ -semiprime submodule if $r{\in}R$ and $x{\in}M$ with $r^2x{\in}P{\setminus}{\phi}(P)$ implies that $rx{\in}P$ . In this paper, we investigate some properties of this class of sub-modules. Also, some characterizations of ${\phi}$ -semiprime submodules are given.

Keywords

semiprime submodules; ${\phi}$ -semiprime submodules; weakly semiprime submodules; m-almost semiprime submodules; flat modules;

Citations & Related Records

Reference

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