Definition:Homogeneous Element/Graded Module

Definition
Let $G \in \set {\N, \Z}$.

Let $R$ be a $G$-graded commutative ring with unity.

Let $M = \bigoplus_{n \in G} M_n$ be a $G$-graded $R$-module.

$x \in M$ is a homogeneous element :
 * $x \in M_n$ for an $n \in G$