An elementary approach to Wedderburn's structure theory. (Q2654164)

\textit{J. H. M. Wedderburn} [London M. S. Proc. (2) 6, 77-118 (1908; JFM 39.0139.01)] proved that a finite-dimensional simple algebra is isomorphic to a matrix algebra over a division algebra. Since then various versions of this result have appeared in the literature and in many algebra textbooks. In this short note, Brešar provides a simple proof for Wedderburn's theorem on the structure of finite-dimensional (semi-)simple algebras. This approach is direct and the presented proof only uses the most elementary tools.