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

DOI:
https://doi.org/10.1090/S0002-9939-96-03095-X

MathSciNet review:
1301519

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Abstract | References | Similar Articles | Additional Information

Abstract: Assume is a polynomial ring over a field and is a homogeneous Gorenstein ideal of codimension and initial degree . We prove that the number of minimal generators of that are of degree is bounded above by , which is the number of minimal generators of the defining ideal of the extremal Gorenstein algebra of codimension and initial degree . Further, is itself extremal if .

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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