Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical

Abstract

his paper is about rings R for which every element is a sum of a tripotent and an element from the Jacobson radical J(R). These rings are called semi-tripotent rings. Examples include Boolean rings, strongly nil-clean rings, strongly 2-nil-clean rings, and semi-boolean rings. Here, many characterizations of semi-tripotent rings are obtained. Necessary and sufficient conditions for a Morita context (respectively, for a group ring of an abelian group or a locally unite nilpotent group) to be semi-tripotent are proved.