Some Counterexamples in Ring Theory
Santosh Kumar Pandey
TL;DR
This paper presents counterexamples and additional results in ring theory, specifically addressing the structure of weakly tripotent rings and challenging previous theorems in the field.
Contribution
It provides counterexamples to a known structure theorem for commutative weakly tripotent rings and offers new results to refine existing understanding.
Findings
Counterexamples to the structure theorem for commutative weakly tripotent rings
Additional results that improve previous findings in ring theory
Clarification of properties related to weakly tripotent rings
Abstract
In this note we provide important and significant observations in ring theory related to weakly tripotent rings. We provide counterexamples for the structure theorem for commutative weakly tripotent rings appeared in arXiv (2017) and Bull. Korean Math. Soc.(2018). Also we give some additional results to improve the existing results.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra