On graded 1-absorbing prime ideals


Abu-Dawwas R., YILDIZ E., TEKİR Ü., KOÇ S.

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1007/s40863-021-00218-3
  • Journal Name: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Keywords: Graded 1-absorbing prime ideal, Graded prime ideal, Graded primary ideal, Graded 2-absorbing ideal

Abstract

Let G be a group with identity e and R be a G-graded commutative ring with unity 1. In this article, we introduce and study the concept of graded 1-absorbing prime ideals which is a generalization of graded prime ideals. A proper graded ideal P of R is called graded 1-absorbing prime if for all nonunit elements x,y,z is an element of h(R) such that xy z is an element of P, then either xy is an element of P or z is an element of P.