Sums of Square-Zero Infinite Matrices Revisited

We improve some earlier results and prove that every N×N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {N}\times \mathbb {N}$$\end{document} column finite matrix over a field of characteristic different from 2 is a sum of at most 10 square-zero matrices.