Reduction numbers and initial ideals

Author:
Aldo Conca

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1015-1020

MSC (2000):
Primary 13P10, 13A30; Secondary 13F20

DOI:
https://doi.org/10.1090/S0002-9939-02-06607-8

Published electronically:
June 12, 2002

MathSciNet review:
1948090

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Abstract | References | Similar Articles | Additional Information

Abstract: The reduction number of a standard graded algebra is the least integer such that there exists a minimal reduction of the homogeneous maximal ideal of such that . Vasconcelos conjectured that where is the initial ideal of an ideal in a polynomial ring with respect to a term order. The goal of this note is to prove the conjecture.

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Additional Information

**Aldo Conca**

Affiliation:
Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, I-16146 Genova, Italia

Email:
conca@dima.unige.it

DOI:
https://doi.org/10.1090/S0002-9939-02-06607-8

Keywords:
Gr\"obner bases,
initial ideal,
reduction number,
Lex-segment ideal

Received by editor(s):
September 24, 2001

Received by editor(s) in revised form:
October 29, 2001

Published electronically:
June 12, 2002

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2002
American Mathematical Society