Danchev, PeterGarcía, EstherGómez Lozano, Miguel2023-11-132023-11-132023-08-24Electronic Journal of Linear Algebra, ISSN 1081-3810, Volume 39, pp. 460-471, August 2023.1081-3810https://hdl.handle.net/10115/25913For any $n\ge 2$ and fi xed $k\ge 1$, we give necessary and suficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k = 0$ over an arbitrary fi eld $\mathbb{F}$.engAttribution 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Matrices, Nilpotents, Units, Ranksinfo:eu-repo/semantics/article10.13001/ela.2023.7851info:eu-repo/semantics/openAccess