A New Characterization of Semi-Tripotent Rings
Ahmad Moussavi, Peter Danchev, Arash Javan, Omid Hasanzadeh
TL;DR
This paper provides a comprehensive characterization of semi-tripotent rings, including conditions for group rings, offering new insights and descriptions of their algebraic structure.
Contribution
It introduces a novel and detailed characterization of semi-tripotent rings and explores their structure, especially in the context of group rings, extending prior work.
Findings
New characterization of semi-tripotent rings
Complete description via sums and products of special elements
Conditions for group rings to be semi-tripotent
Abstract
We give a comprehensive study of the so-called \textit{semi-tripotent rings} obtaining their new and non-trivial characterization as well as a complete description in terms of sums and products of some special elements. Particularly, we explore in-depth when a group ring is semi-tripotent. Our results somewhat supply those established by Koan et al. in Can. Math. Bull. (2019).
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras