Finite generation of Noetherian graded rings
Authors: Shiro Goto and Kikumichi Yamagishi
Journal: Proc. Amer. Math. Soc. 89 (1983), 41-44
MSC: Primary 13E05; Secondary 13E15
MathSciNet review: 706507
Abstract: Let be an additive abelian group. Then a commutative ring is said to be -graded if there is given a family of subgroups of such that and for all , . In this note it is proved, provided is finitely generated, that an -graded ring is Noetherian if and only if the ring is Noetherian and the -algebra is finitely generated. This is not true in general unless is finitely generated. A counterexample is given.