2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64954Using symmetric algebras we simplify (and slightly strengthen) the Bruns-Eisenbud-Evans "generalized principal ideal theorem" on the height of order ideals of non-minimal generators in a module. We also obtain a simple proof and an extension of a result by Kwieciński, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.6 pages, LaTeXCommutative AlgebraAlgebraic Geometry13C15, 13C40; 13D10text