Set of Ring Elements forming Zero Product with given Element is Ideal

Theorem
Let $R$ be a commutative ring.

Let $a \in R$ be an arbitrary element of $R$.

Let $A$ be the subset of $R$ defined as:


 * $A = \set {x \in R: x \circ a = 0_R}$

Then $A$ is an ideal of $A$.

Proof
From Test for Ideal: