The reduction number of an ideal and the local cohomology of the associated graded ring

Author:
Thomas Marley

Journal:
Proc. Amer. Math. Soc. **117** (1993), 335-341

MSC:
Primary 13D45; Secondary 13D40, 13H15

DOI:
https://doi.org/10.1090/S0002-9939-1993-1112496-7

MathSciNet review:
1112496

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Abstract: Let be a local ring and an -primary ideal. A result of Trung shows that if the local cohomology of satisfies certain conditions, then the reduction number of is independent of the minimal reduction chosen. These conditions consist of inequalities. We show that if is Cohen-Macaulay, then one of these inequalities is always satisied, while another can often be easily checked. Applications are then given in two-dimensional Cohen-Macaulay rings. For instance, we show that if the Hilbert function of equals the Hilbert polynomial of for all integers greater than , then the reduction number is independent of the choice of minimal reduction.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1112496-7

Keywords:
Local cohomology,
reduction,
Hilbert function

Article copyright:
© Copyright 1993
American Mathematical Society