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arXiv · 2401.16061

An Extension of Semicommutative Rings via Reflexivity

Sanjiv Subba·Tikaram Subedi
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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.

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BibTeXRIS

Sanjiv Subba, Tikaram Subedi. 2024-01-29. An Extension of Semicommutative Rings via Reflexivity. https://arxiv.org/abs/2401.16061

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