## Definition ## A __ring__ is an [[unital Z-algebra|unital $\mathbb{Z}$-algebra]] $(A, +, -, 0, \cdot, 1)$ with * an associative identity for $\cdot$ $$m_\alpha:\prod_{(a:G)} \prod_{(b:G)} \prod_{(c:G)} (a\cdot b)\cdot c = a\cdot (b\cdot c)$$ ## Examples ## * Every [[contractible type]] is a ring. * The [[integers]] are a ring. * The [[rational numbers]] are a ring. ## See also ## * [[unital Z-algebra]] * [[commutative ring]] * [[cancellation ring]] * [[power function]] * [[polynomial function]]