## A note on generators of least degree in Gorenstein ideals

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- by Matthew Miller and Rafael H. Villarreal PDF
- Proc. Amer. Math. Soc.
**124**(1996), 377-382 Request permission

## Abstract:

Assume $R$ is a polynomial ring over a field and $I$ is a homogeneous Gorenstein ideal of codimension $g\ge 3$ and initial degree $p\ge 2$. 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 $\nu (I_p)=\nu _0$.## References

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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
- 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
- © Copyright 1996 American Mathematical Society
- 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