On A Generalization of Weak Armendariz Rings
Mahboubeh Sanaei, Shervin Sahebi, Hamid H. S. Javadi
TL;DR
This paper introduces J-Armendariz rings, a new generalization of weak Armendariz rings, and explores their properties, including examples of local rings that are and are not weak Armendariz.
Contribution
The paper defines J-Armendariz rings, broadening the class of rings studied, and provides examples distinguishing them from weak Armendariz rings.
Findings
Any local ring is J-Armendariz.
Existence of local rings that are not weak Armendariz.
Abstract
We introduce the notion of J-Armendariz rings, which are a generalization of weak Armendariz rings and investigate their properties. We show that any local ring is J-Armendariz, and then fined a local ring that is not weak Armendariz.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models