Definition 10.39.3. Let $R$ be a ring. Let $M$ be an $R$-module.

1. Given an element $m \in M$ the annihilator of $m$ is the ideal

$\text{Ann}_ R(m) = \text{Ann}(m) = \{ f \in R \mid fm = 0\} .$
2. The annihilator of $M$ is the ideal

$\text{Ann}_ R(M) = \text{Ann}(M) = \{ f \in R \mid fm = 0\ \forall m \in M\} .$

There are also:

• 2 comment(s) on Section 10.39: Supports and annihilators

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).