English

An Extension of Semicommutative Rings via Reflexivity

Rings and Algebras 2024-01-30 v1

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.

Keywords

Cite

@article{arxiv.2401.16061,
  title  = {An Extension of Semicommutative Rings via Reflexivity},
  author = {Sanjiv Subba and Tikaram Subedi},
  journal= {arXiv preprint arXiv:2401.16061},
  year   = {2024}
}