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On graded NR-clean rings

Ismail Namrok

Abstract

This paper presents an extension of the concept of NR-clean introduced in [12] to graded ring theory. We define and explore graded NR-clean rings, which generalize the class of graded U-nil clean previously studied in [15]. We provide examples and basic properties of such rings, and investigate their extensions to including matrix rings, group rings, as well as trivial ring extensions.

On graded NR-clean rings

Abstract

This paper presents an extension of the concept of NR-clean introduced in [12] to graded ring theory. We define and explore graded NR-clean rings, which generalize the class of graded U-nil clean previously studied in [15]. We provide examples and basic properties of such rings, and investigate their extensions to including matrix rings, group rings, as well as trivial ring extensions.
Paper Structure (5 sections, 16 theorems, 3 equations)

This paper contains 5 sections, 16 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. Graded NR-clean rings
  3. Extensions of graded NR-clean rings
  4. Matrix rings
  5. Group rings and trivial ring extensions

Key Result

Proposition 2.1

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

Theorems & Definitions (35)

  • Definition 2.1
  • Example 2.1
  • Example 2.2
  • Proposition 2.1
  • proof
  • Example 2.3
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • ...and 25 more