Definition:Annihilator of Ideal of Ring/Definition 2

Definition

Let $A$ be a commutative ring with unity.

Let $I \subseteq A$ be an ideal.

The annihilator of $I$ is the ideal quotient:

$\ideal {0 : I}$

where $0$ is the zero ideal.

Also see

• Equivalence of Definitions of Annihilator of Ideal of Ring

• Results about annihilators can be found here.