RT Journal Article
T1 Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence.
A1 Danchev, Peter
A1 García González, Esther
A1 Gómez-Lozano, Miguel Ángel
K1 Anillos (Álgebra)
K1 Números complejos
AB 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.
PB Elsevier
YR 2023
FD 2023-07-10
LK https://hdl.handle.net/10630/27998
UL https://hdl.handle.net/10630/27998
LA eng
NO 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
NO P. Danchev was partially supported by the Bulgarian National Science Fund under Grant KP-06No. 32/1 of December 07, 2019, as well as by the BIDEB 2221 of TÜBÍTAK. 2 E. García was partially supported by Ayuda Puente 2022, URJC. 3 M. Gómez were partially supported by the Junta de Andalucía FQM264.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026