On the union of graded prime ideals

Uregen R. N., TEKİR Ü., Oral K. H.

OPEN PHYSICS, vol.14, no.1, pp.114-118, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1515/phys-2016-0011
  • Journal Name: OPEN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.114-118
  • Keywords: graded ring, graded prime ideal, COPRIMELY PACKED RINGS
  • Marmara University Affiliated: Yes

Abstract

In this paper we investigate graded compactly packed rings, which is defined as; if any graded ideal I of R is contained in the union of a family of graded prime ideals of R, then I is actually contained in one of the graded prime ideals of the family. We give some characterizations of graded compactly packed rings. Further, we examine this property on h - Spec(R). We also define a generalization of graded compactly packed rings, the graded coprimely packed rings. We show that R is a graded compactly packed ring if and only if R is a graded coprimely packed ring whenever R be a graded integral domain and h - dim R = 1.