Saturation of a submodule

Question

Let $R$ be an integral domain, $M$ a left $R$-module and $N$ a $R$-submodule of $M$. What is the definition of $\operatorname{sat}_M(N)$?

Answer 1

Let $S$ be some multiplicative closed subset in $R$. Then $\text{sat}_S(N)$ is defined usually as the set of $m \in M$ such that there is an $s \in S$ with $sm \in N$. This is called the $S$-saturation of $N$ in $M$.

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