On the graded-Gelfand commutative rings

Abstract

This paper deals with the graded commutative rings in which every graded prime ideal is contained in a unique graded-maximal ideal called graded-Gelfand ring. The purpose is to establish some topological and algebraic characterizations of these rings, one of which is the algebraic analogue of Urysohn’s lemma. Finally, we look at a special class of those graded rings called graded-ordered rings which can be viewed as graded rings with a Gelfand strong property.