Algebra
《Algebra》 · 第 417 页 · Section IX.1「Simple and Primitive Rings」，Theorem 1.4 及其后定义句
Let $B$ be a subset of a left module $A$ over a ring $R$. Then $\mathfrak{a}(B)=\{r\in R\mid rb=0\text{ for all }b\in B\}$ is a left ideal of $R$. If $B$ is a submodule of $A$, then $\mathfrak{a}(B)$ is an ideal. $\mathfrak{a}(B)$ is called the (left) annihilator of $B$. The right annihilator of a right module is defined analogously.