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On graded u-nil clean rings

Ismail Namrok

Abstract

In this paper we introduce and study the class of graded U-nil clean rings, as a generalization of graded nil-good class defined in [3]. We also investigate the transfer of the graded U-nil cleaness to matrix rings, and to graded group rings as well. The question of when trivial ring extensions are graded U-nil clean is also investigated.

On graded u-nil clean rings

Abstract

In this paper we introduce and study the class of graded U-nil clean rings, as a generalization of graded nil-good class defined in [3]. We also investigate the transfer of the graded U-nil cleaness to matrix rings, and to graded group rings as well. The question of when trivial ring extensions are graded U-nil clean is also investigated.
Paper Structure (7 sections, 16 theorems, 1 equation)

This paper contains 7 sections, 16 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graded U-nil clean rings
  4. Extensions of graded U-nil clean rings
  5. Trivial ring extensions
  6. Group rings
  7. Matrix rings

Key Result

Proposition 3.1

Let $R=\oplus_{g\in G}R_g$ be a $G$-graded U-nil clean ring. Then,

Theorems & Definitions (36)

  • Definition 3.1
  • Remark 3.1
  • Example 3.1
  • Example 3.2
  • Proposition 3.1
  • proof
  • Example 3.3
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • ...and 26 more