2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58951Using Maruyama's theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.13 pages, major revision, to appear in Math. AnnAlgebraic GeometryCommutative Algebra13A20, 14J17,14J60, 16H05text