2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128371We give a simpler proof as well as a generalization of the main result of an article of Shestakov and Umirbaev. This latter article being the first of two that solve a long-standing conjecture about the non-tameness, or "wildness", of Nagata's automorphism. As corollaries we get interesting informations about the leading terms of polynomials forming an automorphism in any dimension and reprove the tameness of automorphisms in dimension two.4 pagesCommutative AlgebraAlgebraic Geometry13F20;13P10;14R10text