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

Authors: WENDE LI, JIANLONG CHEN, YUKUN ZHOU

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

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