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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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Depth of edge rings arising from finite graphs
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by Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura and Augustine B. O’Keefe PDF
Proc. Amer. Math. Soc. 139 (2011), 3807-3813 Request permission

Abstract:

Let $G$ be a finite graph and $K[G]$ the edge ring of $G$. Based on the technique of Gröbner bases and initial ideals, it will be proved that, given integers $f$ and $d$ with $7 \leq f \leq d$, there exists a finite graph $G$ on $[d] = \{ 1, \ldots , d \}$ with $\textrm {depth} K[G] = f$ and with $\textrm {Krull-dim} K[G] = d$.
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Additional Information
  • Takayuki Hibi
  • Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • MR Author ID: 219759
  • Email: hibi@math.sci.osaka-u.ac.jp
  • Akihiro Higashitani
  • Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • Email: sm5037ha@ecs.cmc.osaka-u.ac.jp
  • Kyouko Kimura
  • Affiliation: Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan
  • Email: skkimur@ipc.shizuoka.ac.jp
  • Augustine B. O’Keefe
  • Affiliation: Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
  • Email: aokeefe@tulane.edu
  • Received by editor(s): September 8, 2010
  • Published electronically: April 7, 2011
  • Additional Notes: The fourth author had summer support provided by the JSPS Research Fellowships for Young Scientists and the NSF East Asia and Pacific Institutes Fellowship.
  • Communicated by: Irena Peeva
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3807-3813
  • MSC (2010): Primary 13P10
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11083-9
  • MathSciNet review: 2823027