Let $R$ be a ring which is not necessarily commutative.

Let $M$ be a left $R$-module, let $N$ be a left $R$-submodule of $M$, and let $m$ be an element of $M$.

Let ${\rm Ann}(N)=\{r\in R\mid rn=0, \;{\rm for\;all}\; n\in N\}$ and let ${\rm Ann}(m)=\{r\in R\mid rm=0\}$.

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