Definition:Trivial Module

Definition
Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e_G$.

Let $\left({R, +_R, \circ_R}\right)$ be a ring.

Let $\circ$ be defined as:
 * $\forall \lambda \in R: \forall x \in G: \lambda \circ x = e_G$

Then $\left({G, +_G, \circ}\right)_R$ is an $R$-module.

Such a module is called a trivial module.

Also see

 * Trivial Module is Module
 * Trivial Module is Not Unitary