Integral domain

In ring theory, an integral domain is a commutative ring in which there are no non-trivial zero divisors: that is the product of non-zero elements is again non-zero. The term entire ring is sometimes used.

Properties

 * A commutative ring is an integral domain if and only if the zero ideal is prime.
 * A ring is an integral domain if and only if it is isomorphic to a subring of a field.