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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simple proof of some generalized principal ideal theorems


Authors: David Eisenbud, Craig Huneke and Bernd Ulrich
Journal: Proc. Amer. Math. Soc. 129 (2001), 2535-2540
MSC (2000): Primary 13C15, 13C40; Secondary 13D10
Published electronically: February 22, 2001
MathSciNet review: 1838374
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Abstract:

Using symmetric algebras we simplify $($and slightly strengthen$)$ the Bruns-Eisenbud-Evans ``generalized principal ideal theorem'' on the height of order ideals of nonminimal generators in a module. We also obtain a simple proof and an extension of a result by Kwiecinski, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.


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Additional Information

David Eisenbud
Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Email: de@msri.org

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: huneke@math.ukans.edu

Bernd Ulrich
Affiliation: Department of Mathematics, Michigan State University, E. Lansing, Michigan 48824
Email: ulrich@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05877-4
PII: S 0002-9939(01)05877-4
Keywords: Height, order ideals, determinantal ideals, symmetric algebras, equidimensionality
Received by editor(s): September 21, 1999
Received by editor(s) in revised form: January 14, 2000
Published electronically: February 22, 2001
Additional Notes: The authors are grateful to the NSF and to MSRI for support.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society