On Graded φ-1-absorbing prime ideals

Refai M., Abu-Dawwas R., TEKİR Ü., KOÇ S., Awawdeh R., YILDIZ YILMAZ E.

Proceedings of the Jangjeon Mathematical Society, vol.27, no.2, pp.205-217, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.17777/pjms2024.27.2.205
  • Journal Name: Proceedings of the Jangjeon Mathematical Society
  • Journal Indexes: Scopus, zbMATH
  • Page Numbers: pp.205-217
  • Keywords: graded 1-absorbing prime ideal, graded Ø-1-absorbing prime ideal, Graded Ø-prime ideal
  • Yıldız Technical University Affiliated: Yes

Abstract

Let G be a group, R be a G-gradcd commutative ring with nonzero unity and GI(R) be the set of all graded ideals of R. Suppose that Ø: GI(R) G/(R) u {Ø} is a function. In this article, we introduce and study the concept of graded Ø-1-absorbing prime ideals. A proper graded ideal I of R is called a graded Ø-1-absorbing prime ideal of R if whenever a, b, c: are homogeneous nonunit elements of R such that abc € I — Ø(I), then ab G I or c t I. Several properties of graded Ø-1-a.bsorbing prime ideals have been examined.