## Definition ## A __discrete field__ is a [[discrete 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 discrete field. ## See also ## * [[ring]] * [[field (ring theory)|field]]