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

ISBN

License

ARR

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