Homotopy Type Theory Z-algebra > history (Rev #5)

1. Definition

A $\mathbb{Z}$-algebra is an abelian group $(A, +, -, 0)$ with a bilinear function $(-)\cdot(-): A \times A \to A$

2. Examples

• Every contractible type is a $\mathbb{Z}$-algebra.

• The integers are a $\mathbb{Z}$-algebra.

• The rational numbers are a $\mathbb{Z}$-algebra.

3. See also

• abelian group

• unital Z-algebra

• cancellation Z-algebra

• division Z-algebra

• algebra (ring theory)