Annihilator

Last updated January 27, 2022

Definition

Let $R$ be a ring and $M$ an $R$-module.

Definition. The annihilator of a subset $S\subset M$ is the set of elements in $R$ which yield 0 when multiplied by any element in $S$. These elements form an ideal. $$\text{Ann}(S)={a\in A \mid a\cdot m=0}.$$