Localization and Catenarity in Strongly Graded Rings

The objective of this article is the study of localization and catenarity in strongly G-graded rings with Noetherian base ring, where G is a finitely generated, nilpotent and torsionfree group. We generalize some results of Guédénon (2000 Guédénon , T. ( 2000 ). Anneaux munis d'une action de groupe superrésoluble . Algebras Groups and Geometries 17 : 17 – 48 . [CSA]  [Google Scholar]). It follows from Corollary 2.6 that if G is free Abelian of finite rank and A is a commutative strongly G-graded ring with base ring a Noetherian regular integral domain, then A is a Noetherian regular integral domain.