\begin{definition}[Definition:Annihilator]
Let $R$ be a commutative ring.
Let $M$ and $N$ be modules over $R$.
Let $B : M \times N \to R$ be a bilinear mapping.
The '''annihilator of $D \subseteq M$''', denoted $\map {\operatorname {Ann}_N} D$ is the set:
:$\set {n \in N : \forall d \in D: \map B {d, n} = 0}$
\end{definition}