Definition:Integral Domain

An integral domain $$\left({R, +, \circ,}\right)$$ is a:


 * commutative ring;
 * with a unity
 * in which there are no divisors of zero, that is:

$$\forall x, y \in R: x \circ y = 0_R \Longrightarrow x = 0_R \lor y = 0_R$$

... or alternatively, in which all non-zero elements are cancellable (which is an equivalent statement from Zero Divisor Not Cancellable).