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

Part of: Conditions on elements Rings and algebras arising under various constructions

Published online by Cambridge University Press:  15 March 2019

M. Tamer Koşan ,
Tülay Yildirim  and
Y. Zhou
M. Tamer Koşan
Affiliation:
Department of Mathematics, Gazi University, Ankara, Turkey Email: mtamerkosan@gazi.edu.tr
Tülay Yildirim
Affiliation:
Department of Mathematics, Gebze Technical University, Gebze/Kocaeli, Turkey Email: tyildirim@gtu.edu.tr
Y. Zhou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St.John’s, NL A1C 5S7, Canada Email: zhou@mun.ca
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Abstract

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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.

Keywords

idempotenttripotentJacobson radicalidempotent lifting modulo Jacobson radicalBoolean ringsemi-boolean ring

MSC classification

Primary: 16U99: None of the above, but in this section
Secondary: 16S34: Group rings , Laurent polynomial rings

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 4 , December 2019 , pp. 810 - 821
Copyright
© Canadian Mathematical Society 2019 

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