2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171272In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. In the present paper, we reconstruct their theory by using the "generalized Shestakov-Umirbaev inequality", which was recently given by the author. As a consequence, we obtain a more precise tameness criterion for polynomial automorphisms. In particular, we show that no tame automorphism of a polynomial ring admits a reduction of type IV.52 pagesCommutative AlgebraAlgebraic Geometry14R10text