## Definition ## A __commutative ring__ is a [[ring]] $(A, +, -, 0, \cdot, 1)$ with * a commutative identity for $\cdot$ $$m_\kappa:\prod_{(a:A)} \prod_{(b:A)} a\cdot b = b\cdot a$$ ## Examples ## * Every [[contractible type]] is a commutative ring. * The [[integers]] are a commutative ring. * The [[rational numbers]] are a commutative ring. ## See also ## * [[ring]] * [[rational numbers]] ## References * [[Frank Quinn]], *Proof Projects for Teachers* ([pdf](https://personal.math.vt.edu/fquinn/education/pfs4teachers0.pdf)) category: not redirected to nlab yet