A simple proof of some generalized principal ideal theorems
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- by David Eisenbud, Craig Huneke and Bernd Ulrich PDF
- Proc. Amer. Math. Soc. 129 (2001), 2535-2540 Request permission
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 Kwieciński, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.References
- Winfried Bruns, The Eisenbud-Evans generalized principal ideal theorem and determinantal ideals, Proc. Amer. Math. Soc. 83 (1981), no. 1, 19–24. MR 619972, DOI 10.1090/S0002-9939-1981-0619972-3
- D. Eisenbud: Commutative Algebra with a View Toward Algebraic Geometry. Springer Verlag, 1995.
- David Eisenbud and E. Graham Evans Jr., A generalized principal ideal theorem, Nagoya Math. J. 62 (1976), 41–53. MR 409440, DOI 10.1017/S0027763000024740
- D. Eisenbud, C. Huneke, and B. Ulrich: Order ideals and a generalized Krull height theorem. Preprint.
- D. Eisenbud, C. Huneke, and B. Ulrich: Heights of ideals of minors. In preparation.
- C. Huneke and M. Rossi, The dimension and components of symmetric algebras, J. Algebra 98 (1986), no. 1, 200–210. MR 825143, DOI 10.1016/0021-8693(86)90023-2
- M. Johnson: Equidimensional symmetric algebras and residual intersections. Preprint.
- MichałKwieciński, Bounds for codimensions of Fitting ideals, J. Algebra 194 (1997), no. 2, 378–382. MR 1467157, DOI 10.1006/jabr.1996.6999
- Jean-Pierre Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin-New York, 1965 (French). Cours au Collège de France, 1957–1958, rédigé par Pierre Gabriel; Seconde édition, 1965. MR 0201468, DOI 10.1007/978-3-662-21576-0
- Wolmer V. Vasconcelos, Arithmetic of blowup algebras, London Mathematical Society Lecture Note Series, vol. 195, Cambridge University Press, Cambridge, 1994. MR 1275840, DOI 10.1017/CBO9780511574726
Additional Information
- David Eisenbud
- Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
- MR Author ID: 62330
- ORCID: 0000-0002-5418-5579
- Email: de@msri.org
- Craig Huneke
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- MR Author ID: 89875
- Email: huneke@math.ukans.edu
- Bernd Ulrich
- Affiliation: Department of Mathematics, Michigan State University, E. Lansing, Michigan 48824
- MR Author ID: 175910
- Email: ulrich@math.msu.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2535-2540
- MSC (2000): Primary 13C15, 13C40; Secondary 13D10
- DOI: https://doi.org/10.1090/S0002-9939-01-05877-4
- MathSciNet review: 1838374