On n -1-absorbing prime ideals

Ulucak G., KOÇ S., TEKİR Ü.

Journal of Algebra and its Applications, vol.22, no.10, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219498823502079
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: 1-absorbing prime ideal, n -1-absorbing prime ideal, Prime ideal
  • Marmara University Affiliated: Yes

Abstract

In this paper, we introduce and study n-1-absorbing prime ideals of commutative rings. Let R be a ring and n a positive integer. A proper ideal I of R is said to be an n-1-absorbing prime ideal if whenever x1x2...xn+1 I for some nonunits x1,x2,...,xn+1 R, then either x1x2...xn I or xn+1 I. It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of n-1-absorbing prime ideals are given.