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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 | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

  • 1. W. Bruns: The Eisenbud-Evans generalized principal ideal theorem and determinantal ideals. Proc. Amer. Math. Soc. 83 (1981), 19-24. MR 82k:13010
  • 2. D. Eisenbud: Commutative Algebra with a View Toward Algebraic Geometry. Springer Verlag, 1995.
  • 3. D. Eisenbud and E. G. Evans: A generalized principal ideal theorem. Nagoya Math. J. 62 (1976), 41-53. MR 53:13195
  • 4. D. Eisenbud, C. Huneke, and B. Ulrich: Order ideals and a generalized Krull height theorem. Preprint.
  • 5. D. Eisenbud, C. Huneke, and B. Ulrich: Heights of ideals of minors. In preparation.
  • 6. C. Huneke and M. Rossi: The dimension and components of symmetric algebras. J. Algebra 98 (1986), 200-210. MR 87d:13010
  • 7. M. Johnson: Equidimensional symmetric algebras and residual intersections. Preprint.
  • 8. M. Kwiecinski: Bounds for codimensions of Fitting ideals. J. Algebra 194 (1997), 378-382. MR 98m:13018
  • 9. J.-P. Serre: Algèbre locale, multiplicités. Springer Lect. Notes in Math. 11, 1965. MR 34:1352
  • 10. W. Vasconcelos: Arithmetic of blowup algebras. London Math. Soc. Lect. Notes 195, Cambridge Univ. Press, 1994. MR 95g:13005

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Additional Information

David Eisenbud
Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

Bernd Ulrich
Affiliation: Department of Mathematics, Michigan State University, E. Lansing, Michigan 48824

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

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