Axiom:Linear Ring Action Axioms/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 $M$ $\circ$ satisifes the axioms:

These criteria are called the left linear ring action axioms.

Also see

 * Axiom:Right Linear Ring Action Axioms


 * Definition:Left Linear Ring Action