dc.contributor.author | Danchev, Peter | |
dc.contributor.author | García, Esther | |
dc.contributor.author | Gómez Lozano, Miguel | |
dc.date.accessioned | 2023-10-13T09:45:00Z | |
dc.date.available | 2023-10-13T09:45:00Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Peter Danchev, Esther García, Miguel Gómez Lozano, Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence, Linear Algebra and its Applications, Volume 676, 2023, Pages 44-55, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2023.07.005 | es |
dc.identifier.issn | 0024-3795 | |
dc.identifier.uri | https://hdl.handle.net/10115/24863 | |
dc.description | We are deeply indebted to the anonymous referee for the use of weighted directed graphs and their dynamics in the proof of Proposition 2.1. This combinatorial viewpoint has simplified the arguments and made a much clearer and more understandable article. | es |
dc.description.abstract | For n ≥ 2 and fixed k ≥ 1, we study when an endomorphism
f of Fn, where F is an arbitrary field, can be decomposed
as t + m where t is a root of the unity endomorphism and
m is a nilpotent endomorphism with mk = 0. For fields
of prime characteristic, we show that this decomposition
holds as soon as the characteristic polynomial of f is
algebraic over its base field and the rank of f is at least n
k , and we present several examples that show that the
decomposition does not hold in general. Furthermore, we
completely solve this decomposition problem for k = 2
and nilpotent endomorphisms over arbitrary fields (even
over division rings). This somewhat continues our recent
publications in Linear Multilinear Algebra (2022) and Int. | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.rights | Atribución 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | Root of the unity | es |
dc.subject | Nilpotent | es |
dc.subject | Square-zero element | es |
dc.title | Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence | es |
dc.type | info:eu-repo/semantics/article | es |
dc.identifier.doi | 10.1016/j.laa.2023.07.005 | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |