2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68793In this paper, we study superficial elements of an ideal with respect to a module from a geometrical point of view, using blowing-ups. The notion of weak transform is particularly relevant to this study. We use this viewpoint to get a simple proof of a theorem by D. Kirby characterizing those superficial elements. We also indicate how the same result may be algebraically derived from a more recent theorem of Flenner and Vogel.30 09.2003Commutative AlgebraAlgebraic Geometry13H15; 14C17text