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On $\phi$-2-Absorbing Primary Submodules
Razieh Moradi
,
Mahdieh Ebrahimpour
Abstract
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Let $\phi :S(M)\rightarrow S(M)\cup {\emptyset }$ be a function, where $S(M)$ is the set of submodules of $M$. We say that a proper submodule $N$ of $M$ is a $\phi$-2-absorbing primary submodule if $rsx\in N∖\phi(N)$ implies $r x\in N$, or $s x\in N$, or $rs\in \sqrt {(N:M)}$, where $r,s\in R$ and $x\in M$. In this paper, we study $\phi$-2-absorbing primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of $\phi$-2-absorbing primary submodules and we investigate $\phi$-2-absorbing primary submodules of some well-known modules.