On Gelfand graded commutative rings

TL;DR

This paper explores Gelfand graded commutative rings, providing topological and algebraic characterizations, including an algebraic analogue of Urysohn's lemma, and examines a special class called pm$^+$ graded rings.

Contribution

It introduces the concept of Gelfand graded rings, establishes their key properties, and studies the class of pm$^+$ graded rings with a Gelfand strong property.

Findings

Characterization of Gelfand graded rings

Algebraic analogue of Urysohn's lemma for these rings

Introduction and analysis of pm$^+$ graded rings

Abstract

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