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


Kosan M. T., Yildirim T., Zhou Y.

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, vol.62, no.4, pp.810-821, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.4153/s0008439519000092
  • Journal Name: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.810-821
  • Keywords: idempotent, tripotent, Jacobson radical, idempotent lifting modulo Jacobson radical, Boolean ring, semi-boolean ring, EXCHANGE, IDEMPOTENTS
  • Gazi University Affiliated: Yes

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.