Let $R$ be a D24: Ring.
An D21: Algebraic structure $M = (X, +, \times)$ is a module over $R$ if and only if

(i)	$G = (X, +)$ is an D23: Abelian group
(ii)	$\times : R \times G \to G$ is a D274: Left ring action of $R$ on $G$