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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.

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Some Ideals with Large Projective Dimension
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by Giulio Caviglia and Manoj Kummini PDF
Proc. Amer. Math. Soc. 136 (2008), 505-509 Request permission

Abstract:

For an ideal $I$ in a polynomial ring over a field, a monomial support of $I$ is the set of monomials that appear as terms in a set of minimal generators of $I$. Craig Huneke asked whether the size of a monomial support is a bound for the projective dimension of the ideal. We construct an example to show that, if the number of variables and the degrees of the generators are unspecified, the projective dimension of $I$ grows at least exponentially with the size of a monomial support. The ideal we construct is generated by monomials and binomials.
References
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  • Bahman Engheta, Bounds on projective dimension, Ph.D. thesis, University of Kansas, Lawrence, KS, 2005.
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Additional Information
  • Giulio Caviglia
  • Affiliation: Department of Mathematics, University of California, Berkeley, California
  • Email: caviglia@math.berkeley.edu
  • Manoj Kummini
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas
  • MR Author ID: 827227
  • ORCID: 0000-0002-4822-0112
  • Email: kummini@math.ku.edu
  • Received by editor(s): October 16, 2006
  • Received by editor(s) in revised form: February 11, 2007
  • Published electronically: October 25, 2007
  • Communicated by: Bernd Ulrich
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 505-509
  • MSC (2000): Primary 13D05; Secondary 13C15
  • DOI: https://doi.org/10.1090/S0002-9939-07-09159-9
  • MathSciNet review: 2358490