Reverse and Forward Order Law for the (b,c)-inverse
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Date
2024
Authors
Višnjić, Jelena
Stanišev, Ivana
Ke, Yuanyuan
Journal Title
Journal ISSN
Volume Title
Publisher
Univerzitet u Beogradu, Matematički fakultet
Source
Knjiga apstrakata - XV Srpski matematički kongres, 19–22. juna 2024. Beograd, Srbija
Volume
Issue
Abstract
In a ring R it is well known that if a, w ∈ R^(-1), then aw is also invertible and (aw)^−1 =w^−1 a^−1. This property is called the reverse order law. As the reverse order law holds for the classical inverse, the topic of necessary and sufficient conditions for generalized inverses became very often in the past decades.
The similar property, (aw)^−1 = a^−1 w^−1, is known as the forward order law. Contrary to the reverse order law, even if a and w are both invertible, the forward order law is not valid in general.
Here we present results for the reverse order law for the (b, c)-inverse in a unital ring. An equivalent condition for this law to hold for the (b, c)-inverse is derived. 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
(bc)-inverse, Inverse along an element, Reverse order law, Forward order law
Citation
DOI
Scopus
ISSN
ISBN
978-86-7589-191-8
License
ARR