Let $\displaystyle A$ a conmutative ring, $\displaystyle M$ an $\displaystyle A$-module and $\displaystyle J= \{ a \in A: am=0 \forall m \in M \}$

Prove that $\displaystyle J$ is a subring of $\displaystyle A$ and that $\displaystyle M$ is an $\displaystyle R/J$-module with action $\displaystyle (s+J)m=sm$.

thanks!