Axiom:Linear Ring Action Axioms

Definition
Let $R$ be a ring.

Let $M$ be an abelian group.

Left Linear Ring Action Axioms
Let $\circ : R \times M \to M$ be a mapping from the cartesian product $R \times M$.

$\circ$ satisfies the left linear ring action axioms :

Right Linear Ring Action Axioms
Let $\circ : M \times R \to M$ be a mapping from the cartesian product $M \times R$.

$\circ$ satisfies the right linear ring action axioms :

Also see

 * Definition:Linear Ring Action