## Definition ## A __Heyting field__ is a [[Heyting skewfield]] $(A, +, -, 0, \cdot, 1, #)$ with a commutative identity for $\cdot$: $$m_\kappa:\prod_{(a:A)} \prod_{(b:A)} a\cdot b = b\cdot a$$ ## Examples ## * The [[rational numbers]] are a Heyting field. * Every [[discrete field]] is a Heyting field. ## See also ## * [[ring]] * [[field (ring theory)|field]] * [[ordered field]]