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An Extension of Semicommutative Rings via Reflexivity

Sanjiv Subba, Tikaram Subedi

Abstract

This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right) quasi-duo rings, and the class of J-clean rings but is strictly larger than these classes. Additionally, the article investigates a sufficient condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some conditions for NJ-reflexive rings to be reduced. It also explores extensions of NJ-reflexive rings and notes that the NJ-reflexive property may not carry over to polynomial extensions.

An Extension of Semicommutative Rings via Reflexivity

Abstract

This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right) quasi-duo rings, and the class of J-clean rings but is strictly larger than these classes. Additionally, the article investigates a sufficient condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some conditions for NJ-reflexive rings to be reduced. It also explores extensions of NJ-reflexive rings and notes that the NJ-reflexive property may not carry over to polynomial extensions.
Paper Structure (2 sections, 27 theorems)

This paper contains 2 sections, 27 theorems.

Table of Contents

  1. Introduction
  2. NJ-reflexive Rings

Key Result

Proposition 2.3

Let $R$ be an NJ-reflexive ring. Then:

Theorems & Definitions (55)

  • Definition 2.1
  • Example 2.2
  • Proposition 2.3
  • proof
  • Lemma 2.4
  • Lemma 2.5
  • proof
  • Theorem 2.6
  • proof
  • Corollary 2.7
  • ...and 45 more