Graded Weakly 1-absorbing Prime Ideals

Tekir Ü., Koç S., Abu-Dawwas R., Yıldız E.

Cubo-A Mathematical Journal, vol.24, no.2, pp.1-13, 2022 (ESCI)

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2022
  • Journal Name: Cubo-A Mathematical Journal
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.1-13
  • Marmara University Affiliated: Yes

Abstract

In this paper, we introduce and study graded weakly 1- absorbing prime ideals in graded commutative rings. Let G be a group and R be a G-graded commutative ring with a nonzero identity 1 ̸= 0. A proper graded ideal P of R is called a graded weakly 1-absorbing prime ideal if for each nonunits x, y, z ∈ h(R) with 0 ̸= xyz ∈ P, then either xy ∈ P or z ∈ P. We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.