Serviços Personalizados
Journal
Artigo
Indicadores
- Citado por SciELO
- Acessos
Links relacionados
- Citado por Google
- Similares em SciELO
- Similares em Google
Compartilhar
Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Resumo
DANCHEV, Peter V.. Certain Properties of Square Matrices over Fields with Applications to Rings. Rev.colomb.mat. [online]. 2020, vol.54, n.2, pp.109-116. Epub 04-Mar-2021. ISSN 0034-7426. https://doi.org/10.15446/recolma.v54n2.93833.
We prove that any square nilpotent matrix over a field is a difference of two idempotent matrices as well as that any square matrix over an algebraically closed field is a sum of a nilpotent square-zero matrix and a diagonalizable matrix. We further apply these two assertions to a variation of π-regular rings. These results somewhat improve on establishments due to Breaz from Linear Algebra & Appl. (2018) and Abyzov from Siberian Math. J. (2019) as well as they also refine two recent achievements due to the present author, published in Vest. St. Petersburg Univ. - Ser. Math., Mech. & Astr. (2019) and Chebyshevskii Sb. (2019), respectively.
Palavras-chave : Nilpotent matrices; idempotent matrices; Jordan canonical form; algebraically closed fields; super π-regular rings.