## Definition ## A __discrete integral domain__ is a [[commutative discrete cancellation ring]] $(A, +, -, 0, \cdot, 1)$ with a term $p: (0 = 1) \to \emptyset$. ## Examples ## * The [[integers]] are a discrete integral domain. * The [[rational numbers]] are a discrete integral domain * Every [[discrete field]] is a discrete integral domain. ## See also ## * [[ring]] * [[integral domain]]