Definition:Annihilator

Definition
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:


 * $\set {n \in N : \forall d \in D: \map B {d, n} = 0}$