On weakly 1-absorbing prime ideals

Koç S., Tekir Ü., Yıldız E.

RICERCHE DI MATEMATICA, vol.72, no.2, pp.723-738, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s11587-020-00550-4
  • Journal Name: RICERCHE DI MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.723-738
  • Keywords: Weakly prime ideal, 1-absorbing prime ideal, Weakly 2-absorbing ideal, Weakly 1-absorbing prime ideal, Trivial extension, Rings of continuous functions
  • Marmara University Affiliated: Yes

Abstract

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity 1 not equal 0. A proper ideal P of A is said to be a weakly 1-absorbing prime ideal if for every nonunits x, y, z. A with 0 not equal xyz. P, then xy is an element of P or z is an element of P. In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in C( X), which is the ring of continuous functions of a topological space X.