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 language | English |
|---|---|
| Pages (from-to) | 45-56 |
| Number of pages | 12 |
| Journal | Communications of the Korean Mathematical Society |
| Volume | 37 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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