EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 102[116], pp. 133–148 (2017)

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Rings in which the power of every element is the sum of an idempotent and a unit

Huanyin Chen, Marjan Sheibani

Department of Mathematics; Hangzhou Normal University, Hangzhou, China; Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

Abstract: A ring R is uniquely π-clean if the power of every element can be uniquely written as the sum of an idempotent and a unit. We prove that a ring R is uniquely π-clean if and only if for any aR, there exists an integer m and a central idempotent eR such that a m -eJ(R), if and only if R is Abelian; idempotents lift modulo J(R); and R/P is torsion for all prime ideals PJ(R). Finally, we completely determine when a uniquely π-clean ring has nil Jacobson radical.

Keywords: idempotent unit; Jacobson radical; uniquely clean ring; π-uniquely clean rings

Classification (MSC2000): 16S34; 16U60; 16U99; 16E50

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Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.

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