A Simple Proof of some Generalized Principal Ideal Theorems

2002/09/15 by David Eisenbud, Craig Huneke, Bernd Ulrich
Mathematics · #math.AC #math.AG #msc:13C15 #msc:13C40 #msc:13D10

paper · pdf

published as Proceedings of the AMS 129 (2001) 2535--2540 · 6 pages, LaTeX

arxiv created 2002/09/15 · arxiv updated 2009/11/30

Abstract

Using 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.

Related

• On General Principal Symmetric Ideals
• The minimal free resolution of a generic symmetric principal ideal
• Products and powers of principal symmetric ideals
• Order Ideals and a Generalized Krull Height Theorem
• General symmetric ideals