ON QUASI MAXIMAL IDEALS OF COMMUTATIVE RINGS

ALAN M., Kiliç M., KOÇ S., TEKİR Ü.

Comptes Rendus de L'Academie Bulgare des Sciences, vol.76, no.12, pp.1801-1810, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 12
  • Publication Date: 2023
  • Doi Number: 10.7546/crabs.2023.12.01
  • Journal Name: Comptes Rendus de L'Academie Bulgare des Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
  • Page Numbers: pp.1801-1810
  • Keywords: 2-absorbing ideal, maximal ideal, primary ideal, prime ideal, quasi-maximal ideal
  • Marmara University Affiliated: Yes

Abstract

Let R be a commutative ring with 1 ≠ 0. A proper ideal I of R is said to be a quasi maximal ideal if for every a ∈ R - I, either I + Ra = R or I + Ra is a maximal ideal of R. This class of ideals lies between 2-absorbing ideals and maximal ideals which is different from prime ideals. In addition to give fundamental properties of quasi maximal ideals, we characterize principal ideal UN-rings with √02= (0), direct product of two fields, and Noetherian zero dimensional modules in terms of quasi maximal ideals.