Noetherian Rings Graded by an Abelian Group
Noetherian Rings Graded by an Abelian Group
Throughout this paper, all rings are assumed to be commutative with identity.Let $G$ be an Abelian group.We say that a ring $R$ is a G-graded ring, if there exists a family $\{R_{g}\}_{g\in G}$ of additive subgroups of $R$ such that $R=\oplus_{g\in G}R_{g}$ and $R_{g}R_{h}\subset R_{g+h}$ for every $g,$ $h\in G$ …