\(n\)-torsion clean and almost \(n\)-torsion clean matrix rings

DOI10.3103/S1066369X21010047zbMath1476.16037arXiv1912.01104OpenAlexW3130826660MaRDI QIDQ2027917

A. Cîmpean, Peter V. Danchev

Publication date: 28 May 2021

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.01104

zbMATH Keywords

polynomialsfull matrix ringstriangular matrix rings\(n\)-torsion clean ringssimple fields

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Units, groups of units (associative rings and algebras) (16U60) Idempotent elements (associative rings and algebras) (16U40)

Cites Work

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• Nil-clean companion matrices
• On decomposing any matrix as a linear combination of three idempotents
• On sums of idempotent matrices over a field of positive characteristic
• On expressing matrices over \(\mathbb{Z}_2\) as the sum of an idempotent and a nilpotent
• Matrices over finite fields as sums of periodic and nilpotent elements
• The ring \(\operatorname{M}_{8 k + 4}(\mathbb{Z}_2)\) is nil-clean of index four
• On some matrix analogs of the little Fermat theorem
• Nil-clean matrix rings
• Variations on a question concerning the degrees of divisors of \(x^{n}-1\)
• WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS
• 𝑛-torsion clean rings

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