Definition:Integral Domain/Definition 1

Definition
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.

Also see

 * Equivalence of Definitions of Integral Domain