Some Counterexamples in Ring Theory

2022/02/17 by Pandey, Santosh Kumar
#16R50 #16U60 #16U99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2203.02274

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.

Related

• Weakly tripotent rings
• A New Characterization of Semi-Tripotent Rings
• Rings Whose Non-Invertible Elements are Weakly Nil-Clean
• Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean
• Rings and finite fields whose elements are sums or differences of tripotents and potents