n-Torsion Clean Rings

TL;DR

This paper introduces and studies the class of n-torsion clean rings, providing characterizations for abelian and strongly n-torsion clean rings, especially when n is odd, and discusses open questions in the area.

Contribution

It defines the concept of n-torsion clean rings and offers a complete characterization of strongly n-torsion clean rings for odd n, advancing understanding in ring theory.

Findings

Characterization of abelian n-torsion clean rings

Complete characterization of strongly n-torsion clean rings for odd n

Discussion of open problems in the field

Abstract

Let n be an arbitrary natural number. The class of (strongly) n-torsion clean rings is introduced and investigated. Abelian n-torsion clean rings are somewhat characterized and a complete characterization of strongly n-torsion clean rings is given in the case when n is odd. Some open questions are posed at the end.