J. Korean Math. Soc. 2017; 54(4): 1099-1108
Online first article April 11, 2017 Printed July 1, 2017
https://doi.org/10.4134/JKMS.j160075
Copyright © The Korean Mathematical Society.
Mahdieh Ebrahimpour and Fatemeh Mirzaee
Vali-e-Asr University, Shahid Bahonar University
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 semi\-prime submodules, $m$-almost semiprime submodules, flat modules
MSC numbers: Primary 13C05, Secondary 13C13
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