Homotopy Type Theory module > history (Rev #5, changes)

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Definiton

Let $A$ be an abelian group, let $R$ be a commutative ring , . and let${\alpha }_l:R\times A\to A$ \alpha_l:R \times A \to A be is a an left multiplicative$R$ - -module if it comes with an$R$-action on and abelian group homomorphism$\alpha :R\to (A\to A)$ A \alpha:R \to (A \to 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
• bimodule
• algebra (module theory)
• graded module
• vector space?