Definition:Compatible Module Structures

Definition
Let $A$ and $B$ be rings.

Let $\struct {M, +}$ be an abelian group.

Let $* : A \times M \to M$ and $\circledast: B \times M \to M$ be left or right linear ring actions so that:
 * $(1): \quad \struct {M, +, *}$ is a left or right module over $A$
 * $(2): \quad \struct {M, +, \circledast}$ is a left or right module over $B$

Also see

 * Equivalence of Definitions of Compatible Module Structures


 * Definition:Multimodule