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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on generators of least degree
in Gorenstein ideals


Authors: Matthew Miller and Rafael H. Villarreal
Journal: Proc. Amer. Math. Soc. 124 (1996), 377-382
MSC (1991): Primary 13H10; Secondary 13D40
MathSciNet review: 1301519
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Abstract: Assume $R$ is a polynomial ring over a field and $I$ is a homogeneous Gorenstein ideal of codimension $g\ge3$ and initial degree $p\ge2$. We prove that the number of minimal generators $\nu(I_p)$ of $I$ that are of degree $p$ is bounded above by $\nu_0=\binom{p+g-1}{g-1}-\binom{p+g-3}{g-1}$, which is the number of minimal generators of the defining ideal of the extremal Gorenstein algebra of codimension $g$ and initial degree $p$. Further, $I$ is itself extremal if $\nu(I_p)=\nu_0$.


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Additional Information

Matthew Miller
Affiliation: Department of Mathematics University of South Carolina Columbia, South Carolina 29208.
Email: miller@math.sc.edu

Rafael H. Villarreal
Affiliation: Departamento de Matemáticas Escuela Superior de Física y Matemáticas Instituto Politécnico Nacional Unidad Adolfo López Mateos México, D.F. 07300
Email: vila@esfm.ipn.mx

DOI: https://doi.org/10.1090/S0002-9939-96-03095-X
Received by editor(s): June 6, 1994
Received by editor(s) in revised form: August 25, 1994
Additional Notes: The first author was supported by the National Science Foundation.
The second author was partially supported by COFAA–IPN, CONACyT and SNI, México
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society