Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The higher order group inverse in a ring

Liu Dayong, Chen Huanyin

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.

The higher order group inverse in a ring

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.
Paper Structure (3 sections, 13 theorems, 58 equations)

This paper contains 3 sections, 13 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. the $\mathcal{H}$-group inverse
  3. weak $\mathcal{H}$-group inverse

Key Result

Theorem 2.1

Let $a\in R$. Then the following are equivalent:

Theorems & Definitions (29)

  • Definition 1.1
  • Definition 1.2
  • Theorem 2.1
  • proof
  • Corollary 2.2
  • proof
  • Theorem 2.3
  • proof
  • Corollary 2.4
  • proof
  • ...and 19 more