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