Some properties of (b, c)-inverses in rings
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Date
2023
Authors
Višnjić, Jelena
Stanišev, Ivana
Ke, Yuanyuan
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis
Source
Communications in Algebra
Volume
51
Issue
6
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.
Description
Keywords
(bc)-inverse, commuting properties, generalized inverse, reverse order law, unity
Citation
DOI
10.1080/00927872.2023.2166947
Scopus
ISSN
0092-7872
1532-4125
1532-4125
ISBN
License
ARR