On feebly nil-clean rings

Marjan Sheibani Abdolyousefi; Neda Pouyan

Czechoslovak Mathematical Journal (2024)

  • Issue: 1, page 87-94
  • ISSN: 0011-4642

Abstract

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A ring R is feebly nil-clean if for any a ∈ R there exist two orthogonal idempotents e , f ∈ R and a nilpotent w ∈ R such that a = e - f + w . Let R be a 2-primal feebly nil-clean ring. We prove that every matrix ring over R is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.

How to cite

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Sheibani Abdolyousefi, Marjan, and Pouyan, Neda. "On feebly nil-clean rings." Czechoslovak Mathematical Journal (2024): 87-94. <http://eudml.org/doc/299234>.

@article{SheibaniAbdolyousefi2024,
abstract = {A ring $R$ is feebly nil-clean if for any $a\in R$ there exist two orthogonal idempotents $e,f\in R$ and a nilpotent $w\in R$ such that $a=e-f+w$. Let $R$ be a 2-primal feebly nil-clean ring. We prove that every matrix ring over $R$ is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.},
author = {Sheibani Abdolyousefi, Marjan, Pouyan, Neda},
journal = {Czechoslovak Mathematical Journal},
keywords = {orthogonal idempotent matrix; nilpotent matrix; matrix ring; feebly nil-clean ring},
language = {eng},
number = {1},
pages = {87-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On feebly nil-clean rings},
url = {http://eudml.org/doc/299234},
year = {2024},
}

TY - JOUR
AU - Sheibani Abdolyousefi, Marjan
AU - Pouyan, Neda
TI - On feebly nil-clean rings
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 87
EP - 94
AB - A ring $R$ is feebly nil-clean if for any $a\in R$ there exist two orthogonal idempotents $e,f\in R$ and a nilpotent $w\in R$ such that $a=e-f+w$. Let $R$ be a 2-primal feebly nil-clean ring. We prove that every matrix ring over $R$ is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.
LA - eng
KW - orthogonal idempotent matrix; nilpotent matrix; matrix ring; feebly nil-clean ring
UR - http://eudml.org/doc/299234
ER -

References

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