Weakly Classical Prime Submodules
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In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a {\it classical prime submodule}, if for each$m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. We introduce theconcept of ``weakly classical prime submodules'' and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule $N$ of $M$ is a {\it weakly classical prime submodule} if whenever $a,b\in R$ and $m\in M$ with $0\neq abm\in N$,then $am\in N$ or $bm\in N$.
Abstract
In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a {\it classical prime submodule}, if for each$m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. We introduce theconcept of ``weakly classical prime submodules'' and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule $N$ of $M$ is a {\it weakly classical prime submodule} if whenever $a,b\in R$ and $m\in M$ with $0\neq abm\in N$,then $am\in N$ or $bm\in N$.
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