Equivalence Relations Based on (b,c)-Inverses in Rings
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Date
2024
Authors
Stanišev, Ivana
Višnjić, Jelena
Djordjevic, Dragan
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Source
Mediterranean Journal of Mathematics
Volume
21
Issue
1
Abstract
In this paper, we introduce a binary relation in the set of all (b, c)-invertible elements of a ring, defined in the manner like minus, star, sharp, core, and dual core partial orders. We prove that this binary relation is actually an equivalence relation and we investigate some of its properties. Furthermore, we define another equivalence relation on the set of all (b, c)-invertible elements of a ring, as an improvement of the previous mentioned equivalence relation. In addition, the equivalence criteria are given for the equality of (b, c)-related idempotents of two elements and their (b, c)-invertibility is studied.
Description
Keywords
Generalized inverse, (bc)-inverse, equivalence relation, partial order
Citation
DOI
10.1007/s00009-023-02545-5
Scopus
ISSN
1660-5446
ISBN
License
ARR