Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence

DOI10.1016/j.laa.2023.07.005zbMath1525.15008OpenAlexW4383822700MaRDI QIDQ6178769

Peter V. Danchev, Miguel Gómez Lozano, Esther García

Publication date: 5 September 2023

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2023.07.005

zbMATH Keywords

nilpotentweighted directed graphsquare-zero elementroot of the unity

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21) Units, groups of units (associative rings and algebras) (16U60)

Cites Work

• Unnamed Item
• When is every matrix over a ring the sum of two tripotents?
• Canonical forms for torsion matrices
• 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
• Gradings induced by nilpotent elements
• Nonderogatory matrices as sums of idempotent and nilpotent matrices
• Rings over which matrices are sums of idempotent and \(q \)-potent matrices
• Rings with fine nilpotents
• Nil-clean index of \(M_n(\mathbb{F}_2)\)
• 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
• The similarity reduction of matrices over a skew field
• Fine rings: A new class of simple rings
• Rings with fine idempotents
• Decompositions of matrices into potent and square-zero matrices
• On Some Decompositions of Matrices over Algebraically Closed and Finite Fields
• Decompositions of matrices into diagonalizable and square-zero matrices

This page was built for publication: Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence