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2-Clean Rings

Published online by Cambridge University Press:  20 November 2018

Z. Wang  and
J. L. Chen
Z. Wang
Affiliation:
Department of Mathematics, Southeast University, Nanjing, 210096, China e-mail: zhouwang@seu.edu.cnjlchen@seu.edu.cn
J. L. Chen
Affiliation:
Department of Mathematics, Southeast University, Nanjing, 210096, China e-mail: zhouwang@seu.edu.cnjlchen@seu.edu.cn
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Abstract

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$\text{A}$ ring $R$ is said to be $n$-clean if every element can be written as a sum of an idempotent and $n$ units. The class of these rings contains clean rings and $n$-good rings in which each element is a sum of $n$ units. In this paper, we show that for any ring $R$, the endomorphism ring of a free $R$-module of rank at least 2 is 2-clean and that the ring $B\left( R \right)$ of all $\omega \,\times \,\omega$ row and column-finite matrices over any ring $R$ is 2-clean. Finally, the group ring $R{{C}_{n}}$ is considered where $R$ is a local ring.

Keywords

16D7016D4016S502-clean rings2-good ringsfree modulesrow and column-finite matrix ringsgroup rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 145 - 153
Copyright
Copyright © Canadian Mathematical Society 2009

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