The higher order group inverse in a ring
Rings and Algebras
2026-02-17 v1 Functional Analysis
Abstract
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further characterize when a ring element can be expressed as the sum of a higher-order group element and a nilpotent element.
Cite
@article{arxiv.2602.14421,
title = {The higher order group inverse in a ring},
author = {Liu Dayong and Chen Huanyin},
journal= {arXiv preprint arXiv:2602.14421},
year = {2026}
}
Comments
14 pages