Element of Integral Domain Divides Zero

Theorem
Let $$\left({D, +, \circ}\right)$$ be an integral domain whose zero is $$0_D$$.

Then every element of $$D$$ is a divisor of zero:
 * $$\forall x \in D: x \backslash 0_D$$

Proof
By definition, an integral domain is a ring.

So, from Ring Product with Zero:
 * $$\forall x \in D: 0_D = x \circ 0_D$$.

The result follows from the definition of divisor.