Some properties of (b, c)-inverses in rings

Višnjić, Jelena; Stanišev, Ivana; Ke, Yuanyuan

doi:10.1080/00927872.2023.2166947

Article Metadata only M22

2023

Višnjić, Jelena
Stanišev, Ivana
Ke, Yuanyuan

Taylor & Francis

Communications in Algebra

2600

2613

English

M22 - Paper in a prominent international journal

In this paper, we study (b, c)-invertibility of some arbitrary (b, c)-inverse and we give an equivalent condition for its (b, c)-invertibility. Moreover, we investigate when some well known properties of generalized inverses hold for (b, c)-inverses. Further, we study when the (b, c)-inverse of the unity is equal to the unity itself and we obtain equivalent conditions for this to hold. In addition, we investigate the reverse order law for the (b, c)-inverse. Finally, we prove that in the case when the unity is (b, c)-invertible, the set of all (b, c)-inverses, with respect to multiplication, is a group.

(bc)-inverse, commuting properties, generalized inverse, reverse order law, unity

DOI

10.1080/00927872.2023.2166947

ISSN

0092-7872
1532-4125

URI

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

Scopus OpenCitations OpenAlex

dc.rights.license	ARR
dc.rights.uri	All rights reserved
dc.creator	Višnjić, Jelena
dc.creator	Stanišev, Ivana
dc.creator	Ke, Yuanyuan
dc.date.accessioned	2024-12-24T09:31:37Z
dc.date.available	2024-12-24T09:31:37Z
dc.date.issued	2023
dc.identifier.issn	0092-7872
dc.identifier.issn	1532-4125
dc.identifier.doi	10.1080/00927872.2023.2166947
dc.identifier.uri	https://repozitorijum.tfbor.bg.ac.rs/handle/123456789/5926
dc.description.abstract	In this paper, we study (b, c)-invertibility of some arbitrary (b, c)-inverse and we give an equivalent condition for its (b, c)-invertibility. Moreover, we investigate when some well known properties of generalized inverses hold for (b, c)-inverses. Further, we study when the (b, c)-inverse of the unity is equal to the unity itself and we obtain equivalent conditions for this to hold. In addition, we investigate the reverse order law for the (b, c)-inverse. Finally, we prove that in the case when the unity is (b, c)-invertible, the set of all (b, c)-inverses, with respect to multiplication, is a group.
dc.language.iso	en
dc.publisher	Taylor & Francis
dc.source	Communications in Algebra
dc.subject	(bc)-inverse
dc.subject	commuting properties
dc.subject	generalized inverse
dc.subject	reverse order law
dc.subject	unity
dc.title	Some properties of (b, c)-inverses in rings
dc.type	article
dc.type.version	publishedVersion
dc.citation.volume	51
dc.citation.issue	6
dc.citation.spage	2600
dc.citation.epage	2613
dc.citation.rank	M22


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