Definition:Annihilator of Ideal of Ring/Definition 1

Definition

Let $A$ be a commutative ring with unity.

Let $I \subseteq A$ be an ideal.

The annihilator of $I$ is the ideal consisting of the elements $a \in A$ such that:

$\forall x \in I: a \cdot x = 0$

where $0 \in A$ is its zero.

Also see

• Equivalence of Definitions of Annihilator of Ideal of Ring

• Results about annihilators can be found here.