Homotopy Type Theory Z-algebra > history (Rev #7, changes)

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Definition

A $\mathbb{Z}$-algebra is an a abelian $\mathbb{Z}$-module group $(A,+,-,0)$ (A, 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

• characteristic

• unital Z-algebra

• cancellation Z-algebra

• division Z-algebra

• algebra (ring theory)