Weak core and central weak core inverse in a proper $*$-ring
Jajati Keshari Sahoo, Ratikanta Behera, Sourav Das, R. N. Mohapatra · arXiv (Cornell University) · 2020
In this paper, we introduce the notion of weak core and central weak core inverse in a proper $*$-ring. We further elaborate on these two classes by producing a few representations and characterization of the weak core and central weak core invertible elements. We investigate additive properties and a few explicit expressions for these two classes of inverses through other generalized inverses. In addition to these, numerical examples are provided to validate a few claims on weak core inverses.