<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An arbitrary unital ring R is called <italic>feebly nil-clean</italic> if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef = fe. For any commutative ring R and any abelian group G, we find a necessary and sufficient condition when the group ring R(G) is feebly nil-clean only in terms of R, G and their sections. Our result refines establishments due to McGovern et al. in J. Algebra Appl. (2015) on nil-clean rings and Danchev-McGovern in J. Algebra (2015) on weakly nil-clean rings, respectively.</p></abstract>

An arbitrary unital ring R is called feebly nil-clean if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef = fe. For any commutative ring R and any abelian group G, we find a necessary and sufficient condition when the group ring R(G) is feebly nil-clean only in terms of R, G and their sections. Our result refines establishments due to McGovern et al. in J. Algebra Appl. (2015) on nil-clean rings and Danchev-McGovern in J. Algebra (2015) on weakly nil-clean rings, respectively.

Commutative feebly nil-clean group rings

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Commutative feebly nil-clean group rings"}

An arbitrary unital ring R is called feebly nil-clean if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef =...

Commutative feebly nil-clean group rings

Publié en ligne: 27 févr. 2020

Pages: 264 - 270

Reçu: 15 janv. 2019

DOI: https://doi.org/10.2478/ausm-2019-0020

Mots clés
nil-clean rings, weakly nil-clean rings, feebly nil-clean rings, group rings

© 2019 Peter V. Danchev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Commutative feebly nil-clean group rings

Publié en ligne: 27 févr. 2020

Pages: 264 - 270

Reçu: 15 janv. 2019

DOI: https://doi.org/10.2478/ausm-2019-0020

Mots clésnil-clean rings, weakly nil-clean rings, feebly nil-clean rings, group rings

© 2019 Peter V. Danchev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
nil-clean rings, weakly nil-clean rings, feebly nil-clean rings, group rings