## Definition ## A __$\mathbb{Z}$-algebra__ is an [[abelian group]] $(A, +, -, 0)$ with a [[bilinear function]] $(-)\cdot(-): A \times A \to A$ ## Examples ## * Every [[contractible type]] is a $\mathbb{Z}$-algebra. * The [[integers]] are a $\mathbb{Z}$-algebra. * The [[rational numbers]] are a $\mathbb{Z}$-algebra. ## See also ## * [[abelian group]] * [[unital Z-algebra]] * [[cancellation Z-algebra]] * [[division Z-algebra]]