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 $\textrm {Krull-dim} K[G] = d$.References
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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