Equivalence Relations Based on (b,c)-Inverses in Rings

Stanišev, Ivana; Višnjić, Jelena; Djordjevic, Dragan

doi:10.1007/s00009-023-02545-5

Article Metadata only M21

2024

Stanišev, Ivana
Višnjić, Jelena
Djordjevic, Dragan

Springer Nature

Mediterranean Journal of Mathematics

English

M21 - Paper in a top international journal

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.

info:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174007/RS//

Generalized inverse, (bc)-inverse, equivalence relation, partial order

DOI

10.1007/s00009-023-02545-5

ISSN

1660-5446

URI

https://repozitorijum.tfbor.bg.ac.rs/handle/...

Scopus

OpenCitations

dc.rights.license	ARR
dc.identifier.doi	10.1007/s00009-023-02545-5
dc.identifier.uri	https://repozitorijum.tfbor.bg.ac.rs/handle/123456789/5859
dc.description.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.
dc.description.sponsorship	info:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174007/RS//
dc.language.iso	en
dc.publisher	Springer Nature
dc.source	Mediterranean Journal of Mathematics
dc.subject	Generalized inverse
dc.subject	(bc)-inverse
dc.subject	equivalence relation
dc.rights.uri	All rights reserved
dc.subject	partial order
dc.title	Equivalence Relations Based on (b,c)-Inverses in Rings
dc.type	article
dc.type.version	publishedVersion
dc.citation.volume	21
dc.citation.issue	1
dc.citation.spage	11
dc.citation.rank	M21
dc.creator	Stanišev, Ivana
dc.creator	Višnjić, Jelena
dc.creator	Djordjevic, Dragan
dc.date.accessioned	2024-10-04T09:02:00Z
dc.date.available	2024-10-04T09:02:00Z
dc.date.issued	2024
dc.identifier.issn	1660-5446


Equivalence Relations Based on (b,c)-Inverses in Rings	2