On the complexity of the integral closure
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- by Bernd Ulrich and Wolmer V. Vasconcelos PDF
- Trans. Amer. Math. Soc. 357 (2005), 425-442 Request permission
Abstract:
The computation of the integral closure of an affine ring has been the focus of several modern algorithms. We will treat here one related problem: the number of generators the integral closure of an affine ring may require. This number, and the degrees of the generators in the graded case, are major measures of cost of the computation. We prove several polynomial type bounds for various kinds of algebras, and establish in characteristic zero an exponential type bound for homogeneous algebras with a small singular locus.References
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Additional Information
- Bernd Ulrich
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
- MR Author ID: 175910
- Email: ulrich@math.purdue.edu
- Wolmer V. Vasconcelos
- Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019
- Email: vasconce@math.rutgers.edu
- Received by editor(s): May 10, 2002
- Published electronically: September 23, 2004
- Additional Notes: The authors were partially supported by the NSF
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 425-442
- MSC (2000): Primary 13B22; Secondary 13C15, 13H15, 13P10
- DOI: https://doi.org/10.1090/S0002-9947-04-03627-X
- MathSciNet review: 2095616
Dedicated: Dedicated to Aron Simis on the occasion of his sixtieth birthday