2023

Višnjić, Jelena
Stanišev, Ivana 
Ke, Yuanyuan

International Linear Algebra Society

Electronic Journal of Linear Algebra

39

379

394

English

M23 - Paper in an international journal

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.

(b, c)-inverse, inverse along an element, reverse order law, forward order law

DOI

10.13001/ela.2023.7807

ISSN

1081-3810
1537-9582

URI

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