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On the reduction number of some graded algebras

Author(s): Henrik Bresinsky; Lê Tuân Hoa
Journal: Proc. Amer. Math. Soc. 127 (1999), 1257-1263.
MSC (1991): Primary 13C05, 13A15
Posted: January 27, 1999
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Abstract: The main result of the paper confirms, for generic coordinates, a conjecture which states that $r(R/I) \le r(R/in(I))$. Here $I$ is a homogeneous polynomial ideal in $R$ and $r(R/I)$ and $r(R/in(I))$ are the reduction numbers.

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Bresinsky, H., F. Curtis, M. Fiorentini, L. T. Hoa: On the structure of local cohomology modules for monomial curves in $\text{\bf P}^{3}_{k}$, Nagoya Math. J. 136(1994), 81-114. MR 96b:14040
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Gräbe, H. J.: Homology modules and standard bases, Beitr. Alg. Geom. 32(1991), 11-20. MR 93c:13016
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Northcott, D. G., D. Rees: Reductions of ideals in local rings, Proc. Camb. Phil. Soc. 50(1954), 145-158. MR 15:596a
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Additional Information:

Henrik Bresinsky
Affiliation: Department of Mathematics, University of Maine, Orono, Maine 04469-5752
Email: Henrik@maine.maine.edu

Lê Tuân Hoa
Affiliation: Institute of Mathematics, Box 631, Bò Hô, Hanoi, Vietnam

DOI: 10.1090/S0002-9939-99-04622-5
PII: S 0002-9939(99)04622-5
Keywords: Monomial ideal, Borel-fixed ideal, generic coordinates, reduction number
Received by editor(s): April 18, 1997
Received by editor(s) in revised form: August 6, 1997
Posted: January 27, 1999
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1999, American Mathematical Society

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