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 if and only if:

$x \in M_n$ for an $n \in G$

Sources

• 1980: Hideyuki Matsumura: Commutative Algebra $10:$ Graded Ring and Modules