Reverse order law and forward order law for the (b, c)-Inverse
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Date
2023
Authors
Višnjić, Jelena
Stanišev, Ivana
Ke, Yuanyuan
Journal Title
Journal ISSN
Volume Title
Publisher
International Linear Algebra Society
Source
Electronic Journal of Linear Algebra
Volume
39
Issue
Abstract
The reverse order law and the forward order law have been studied for various types of generalized inverses. The (b,c)-inverse is a generalization of some well known generalized inverses, such as the Moore-Penrose inverse, the Drazin inverse, the core inverse, etc. In this paper, the reverse order law for the (b,c)-inverse, in a unital ring, is investigated and an equivalent condition for this law to hold for the (b,c)-inverse is derived. Also, some known results on this topic are generalized. Furthermore, the forward order law for the (b,c)-inverse in a ring with a unity is introduced, for different choices of b and c. Moreover, as corollaries of obtained results, equivalent conditions for the reverse order law and the forward order law for the inverse along an element are derived.
Description
Keywords
(b, c)-inverse, inverse along an element, reverse order law, forward order law
Citation
DOI
10.13001/ela.2023.7807
Scopus
ISSN
1537-9582
1081-3810
1081-3810
ISBN
License
ARR