English

m-weak group inverse in a ring with proper involution

Rings and Algebras 2024-06-25 v1

Abstract

The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and prove that it coincides with its m-weak group invertibility. We present the equivalent characterization of the m-weak group inverse by using a polar-like property. The relations between m-weak group inverse and core-EP inverse are also established. These give some new properties of the weak group inverse for complex matrices and ring elements.

Keywords

Cite

@article{arxiv.2406.15745,
  title  = {m-weak group inverse in a ring with proper involution},
  author = {Huanyin Chen},
  journal= {arXiv preprint arXiv:2406.15745},
  year   = {2024}
}
R2 v1 2026-06-28T17:15:44.739Z