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Rings whose elements are the sum of a tripotent and an element from the Jacobson radical. (English) Zbl 1490.16091

Summary: This 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 finite nilpotent group) to be semi-tripotent are proved.

MSC:

16U99 Conditions on elements
16N20 Jacobson radical, quasimultiplication
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