Characterizations and representations of weak core inverses and $m$-weak group inverses

Authors

WENDE LI
JIANLONG CHEN
YUKUN ZHOU

DOI

10.55730/1300-0098.3440

Abstract

In a ring with an involution, we first present some necessary and sufficient conditions for the existence of the $m$-weak group inverse and expression. As an application, we prove that a regular element $a$ is $(m+1)$-weak group invertible if and only if $a^2a^{-}$ is $m$-weak group invertible, where $a^{-}$ is an inner inverse of $a$. The relevant results for weak core inverses and for pseudocore inverses are given. In addition, we present some new characterizations of weak core inverses, and also investigate maximal classes

Keywords

Weak core inverse, $m$-weak group inverse, weak group inverse, pseudocore inverse

First Page

1453

Last Page

1468

Recommended Citation

LI, WENDE; CHEN, JIANLONG; and ZHOU, YUKUN (2023) "Characterizations and representations of weak core inverses and $m$-weak group inverses," Turkish Journal of Mathematics: Vol. 47: No. 5, Article 11. https://doi.org/10.55730/1300-0098.3440
Available at: https://journals.tubitak.gov.tr/math/vol47/iss5/11