Definition:Linear Ring Action/Right

Definition
Let $R$ be a ring.

Let $M$ be an abelian group. Let $\circ : M \times R \to M$ be a mapping from the cartesian product $M \times R$.

$\circ$ is a right linear ring action of $R$ on $M$ $\circ$ satisfies the right ring action axioms:

Also see

 * Definition:Module over Ring
 * Correspondence between Linear Ring Actions and Ring Representations