A bound on the reduction number

of a primary ideal

Author:
M. E. Rossi

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1325-1332

MSC (1991):
Primary 14M05; Secondary 13H10

DOI:
https://doi.org/10.1090/S0002-9939-99-05393-9

Published electronically:
October 5, 1999

MathSciNet review:
1670423

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a local ring of positive dimension and let be an -primary ideal. We denote the reduction number of by , which is the smallest integer such that for some reduction of In this paper we give an upper bound on in terms of numerical invariants which are related with the Hilbert coefficients of when is Cohen-Macaulay. If , it is known that where denotes the multiplicity of If in Corollary 1.5 we prove where is the first Hilbert coefficient of From this bound several results follow. Theorem 1.3 gives an upper bound on in a more general setting.

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Additional Information

**M. E. Rossi**

Affiliation:
Dipartimento di Matematica, Universita’ di Genova, Via Dodecaneso 35, 16146- Genova, Italy

Email:
rossim@dima.unige.it

DOI:
https://doi.org/10.1090/S0002-9939-99-05393-9

Keywords:
Cohen-Macaulay local ring,
primary ideals,
reduction number,
minimal reduction,
associated graded ring,
Hilbert function,
Hilbert coefficients

Received by editor(s):
July 6, 1998

Published electronically:
October 5, 1999

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2000
American Mathematical Society