Homotopy Type Theory module > history (Rev #1)

Definiton

Let $A$ be an abelian group, let $R$ be a commutative ring, and let $\alpha_l:R \times A \to A$ be a left multiplicative $R$-action on $A$ and $\alpha_r:A \times R \to A$ be a right multiplicative $R$-action on $A$. $A$ is a left $R$-module if $\alpha_l$ is a bilinear function, and $A$ is a right $R$-module if $\alpha_r$ is a bilinear function.

Properties

Every abelian group is a left $\mathbb{Z}$-module and a right $\mathbb{Z}$-module.

See also

• abelian group
• action
• monoid
• algebra (ring theory)