## Definition ## A __commutative discrete cancellation ring__ is a [[discrete cancellation ring]] $(A, +, -, 0, \cdot)$ that is also a [[commutative ring]] ## Examples ## * The [[integers]] are a commutative discrete cancellation ring. * The [[rational numbers]] are a commutative discrete cancellation ring. * Every [[discrete integral domain]] is a commutative discrete cancellation ring. * Every [[commutative discrete division ring]] is a commutative discrete cancellation ring. * Every [[commutative discrete reciprocal ring]] is a commutative discrete cancellation ring. ## See also ## * [[commutative ring]] * [[commutative cancellation ring]]