\begin{definition}[Definition:Integral Domain/Definition 1]
An '''integral domain''' $\struct {D, +, \circ}$ is:
:a commutative ring which is non-null
:with a unity
:in which there are no (proper) zero divisors, that is:
::: $\forall x, y \in D: x \circ y = 0_D \implies x = 0_D \text{ or } y = 0_D$
that is (from the Cancellation Law of Ring Product of Integral Domain) in which all non-zero elements are cancellable.
\end{definition}