# Definition:Trivial Annihilator

## Definition

Let $\left({R, +, \times}\right)$ be a ring or, more usually, a field.

From Annihilator of Ring Always Contains Zero, we have that $0 \in \operatorname{Ann} \left({R}\right)$ whatever the ring $R$ is.

$R$ is said to have a trivial annihilator if and only if its annihilator $\operatorname{Ann} \left({R}\right)$ consists only of the integer $0$.