Definition:Linear Ring Action/Left

Definition
Let $R$ be a ring.

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

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

Also known as
A left ring action is also known as a ring action.

Also see

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