A note on nil-clean rings

Peter V. Danchev

doi:10.2478/ausm-2020-0020

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A note on nil-clean rings

Acta Universitatis Sapientiae, Mathematica

Volume 12 (2020): Issue 2 (November 2020)

By: Peter V. Danchev

Open Access

|Dec 2020

Abstract

We study a special kind of nil-clean rings, namely those nil-clean rings whose nilpotent elements are difference of two “left-right symmetric” idempotents, and prove that in some various cases they are strongly π-regular. We also show that all nil-clean rings having cyclic unit 2-groups are themselves strongly nil-clean of characteristic 2 (and thus they are again strongly π-regular).

References

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2020-0020 | Journal eISSN: 2066-7752

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Language: English

Page range: 287 - 293

Submitted on: Dec 17, 2019

Published online: Dec 2, 2020

Published in print: Nov 1, 2020

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

nil-clean rings,

nilpotents,

idempotents,

strongly π-regular rings

MSC:

16U99,

16E50,

16W10,

13B99

Related subjects:

Mathematics,

General mathematics

© 2020 Peter V. Danchev, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 2 (November 2020)