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A short Note on prime submodules
Let $R$ be a commutative ring with identity and $M$ be a unital $R$-module. A proper submodule $N$ of $M$ with $N:_RM=\frak p$ is said to be prime or $\frak p$-prime ($\frak p$ a prime ideal of $R$) if $rx\in N$ for $r\in R$ and $x\in M$ implies that either …