Group Rings that are Additively Generated by Idempotents and Units

TL;DR

This paper investigates properties of certain group rings, focusing on those generated additively by idempotents and units, and establishes conditions under which these rings have stable range one.

Contribution

It introduces new results on clean group rings and characterizes when group rings over Abelian exchange rings have stable range one.

Findings

Group rings generated additively by idempotents and units are studied.

Proves that group rings over Abelian exchange rings with locally finite groups have stable range one.

Abstract

We study clean group rings and also the group rings whose every element is a sum of two units. We also prove that if R is an Abelian exchange ring and G is a locally finite group, then the group ring RG has stable range one.