2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73416We show that the idea used by Kempf (1990) in order to obtain a splitting criterion for vector bundles on projective spaces leads to an elementary proof of the Babylonian tower theorem for this class of bundles, a result due to Barth--Van de Ven (1974) in the rank 2 case and to Sato (1977) and Tyurin (1976) in the case of arbitrary rank. As a byproduct we obtain a slight improvement of the numerical criterion of Flenner (1985) in the particular case under consideration.LateX2e, 4 pagesAlgebraic Geometry14F05; 14J60text