\begin{definition}[Definition:Annihilator of Ideal of Ring/Definition 1]
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.
\end{definition}