<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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).</p></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).

A note on nil-clean rings

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A note on nil-clean rings"}

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...

A note on nil-clean rings

Online veröffentlicht: 02. Dez. 2020

Seitenbereich: 287 - 293

Eingereicht: 17. Dez. 2019

DOI: https://doi.org/10.2478/ausm-2020-0020

Schlüsselwörter
nil-clean rings, nilpotents, idempotents, strongly π-regular rings

© 2020 Peter V. Danchev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A note on nil-clean rings

Online veröffentlicht: 02. Dez. 2020

Seitenbereich: 287 - 293

Eingereicht: 17. Dez. 2019

DOI: https://doi.org/10.2478/ausm-2020-0020

Schlüsselwörternil-clean rings, nilpotents, idempotents, strongly π-regular rings

© 2020 Peter V. Danchev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
nil-clean rings, nilpotents, idempotents, strongly π-regular rings