Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A note on generators of least degree in Gorenstein ideals
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13H10, 13D40
  • Retrieve articles in all journals with MSC (1991): 13H10, 13D40
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