## Definiton ## Let $A$ be an [[abelian group]], let $R$ be a [[commutative ring]]. $A$ is an $R$-module if it comes with an $R$-[[action]] and abelian group homomorphism $\alpha:R \to (A \to A)$. ## Properties ## Every abelian group is a $\mathbb{Z}$-module. ## See also ## * [[abelian group]] * [[action]] * [[monoid]] * [[algebra (module theory)]] * [[graded module]]