Characterizations and representations of core and dual core inverses

TL;DR

This paper explores properties and representations of core and dual core inverses, including commutativity, reverse order law, and new characterizations via ring invertibilities, enhancing understanding of their algebraic structure.

Contribution

It provides novel characterizations and representations of core and dual core inverses in rings, expanding theoretical understanding of their properties.

Findings

Analysis of double commutativity and reverse order law for core inverse

New characterizations of Moore-Penrose inverse via one-sided invertibilities

Representations of core and dual core inverses of regular elements

Abstract

In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.