Rings In Which Every Ideal Contained In The Set Of Zero-Divisors Is A D-Ideal

Adam Anebri*, Najib Mahdou, Abdeslam Mimouni

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we introduce and study the class of rings in which every ideal consisting entirely of zero divisors is a d-ideal, considered as a generalization of strongly duo rings. Some results including the characterization of AA-rings are given in the First section. Further, we examine the stability of these rings in localization and study the possible transfer to direct product and trivial ring extension. In addition, we define the class of dE-ideals which allows us to characterize von Neumann regular rings.

Original languageEnglish
Pages (from-to)45-56
Number of pages12
JournalCommunications of the Korean Mathematical Society
Volume37
Issue number1
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022. Korean Mathematical Society

Keywords

  • Aa-ring
  • D-ideal
  • De-ideal
  • Direct product
  • Localization
  • Strongly duo ring
  • Trivial ring extension

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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