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march 2018 Generalizing nil clean rings
Peter Danchev
Bull. Belg. Math. Soc. Simon Stevin 25(1): 13-29 (march 2018). DOI: 10.36045/bbms/1523412048

Abstract

We introduce the class of {\it unipotently nil clean} rings as these rings $R$ in which for every $a\in R$ there exist an idempotent $e$ and a nilpotent $q$ such that $a-e-1-q\in (1-e)Ra$. Each unipotently nil clean ring is weakly nil clean as well as each nil clean ring is unipotently nil clean. Our results obtained here considerably extend those from [8] and [7], respectively.

Citation

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Peter Danchev. "Generalizing nil clean rings." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 13 - 29, march 2018. https://doi.org/10.36045/bbms/1523412048

Information

Published: march 2018
First available in Project Euclid: 11 April 2018

zbMATH: 06882538
MathSciNet: MR3784502
Digital Object Identifier: 10.36045/bbms/1523412048

Subjects:
Primary: 16E50 , 16S70 , 16U70 , 16U99

Keywords: $\pi$-regular rings , strongly $\pi$-regular rings , weakly clean rings , weakly nil clean ring

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 1 • march 2018
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