\begin{definition}[Definition:Left Module]
Let $\struct {R, +_R, \times_R}$ be a ring.
Let $\struct {G, +_G}$ be an abelian group.
A left module over $R$ is an $R$-algebraic structure $\struct {G, +_G, \circ}_R$ with one operation $\circ$, the '''(left) ring action''', which satisfies the left module axioms:
{{:Axiom:Left Module Axioms}}
\end{definition}