## Definition ## A __commutative Heyting division ring__ is a [[Heyting division ring]] $(A, +, -, 0, \cdot, 1, #)$ with a commutative identity for $\cdot$: $$m_\kappa:\prod_{(a:A)} \prod_{(b:A)} a\cdot b = b\cdot a$$ ## Properties ## Every commutative Heyting division ring is a [[commutative Heyting reciprocal ring]]. ## Examples ## * The [[rational numbers]] are a commutative Heyting division ring. * Every [[commutative discrete division ring]] is a commutative Heyting division ring. * Every [[commutative Heyting reciprocal ring]] is a commutative Heyting division ring, and thus every [[Heyting field]] is a commutative Heyting division ring. ## See also ## * [[commutative ring]] * [[commutative division ring]]