Periodic and q-potent elements in rings

TL;DR

This paper explores properties of rings involving q-potent and periodic elements, providing results on rings where elements decompose into commuting sums of idempotents and q-potent elements, and examining periodic rings and k-potent elements.

Contribution

It introduces new results on rings with elements decomposable into commuting sums of idempotents and q-potent elements, and studies periodic rings and k-potent elements.

Findings

Rings where every element is a sum of commuting idempotent and q-potent elements

Properties of periodic rings and k-potent elements in algebras

Characterizations of rings with specific element decompositions

Abstract

This paper, we consider some properties of rings via q-potent and periodic elements. In this paper we give some results of rings in which every element is a sum of an idempotent and a q-potent that commute; periodic rings and k-potent elements of algebras.