Let $G$ be any multiplicative group (abelian or not). Suppose that $R$ is a $G$-graded ring, i.e., there exists a family of additive subgroup $\{R_g\}_{g\in G}$ such that $R=\bigoplus_{g\in G}R_g$ and, for all $g,h\in G$, $R_gR_h\subseteq R_{gh}$.
My question:
If $I\subseteq R$ is an ideal (not necessarily graded), what means that $I_{\textrm{gr}}$ is the associated graded ideal of $I$?
Someone could help me with this, please? Thanks.
Sorry for my english.