Graph and depth of a monomial squarefree ideal
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- by Dorin Popescu PDF
- Proc. Amer. Math. Soc. 140 (2012), 3813-3822 Request permission
Abstract:
Let $I$ be a monomial squarefree ideal of a polynomial ring $S$ over a field $K$ such that the sum of every three different ideals of its minimal prime ideals is the maximal ideal of $S$, or more generally a constant ideal. We associate to $I$ a graph on $[s]$, $s=|\operatorname {Min}S/I|$, on which we may read the depth of $I$. In particular, $\operatorname {depth_S}I$ does not depend on char $K$. Also we show that $I$ satisfies Stanley’s Conjecture.References
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Additional Information
- Dorin Popescu
- Affiliation: Institute of Mathematics “Simion Stoilow”, University of Bucharest, P.O. Box 1-764, Bucharest 014700, Romania
- Email: dorin.popescu@imar.ro
- Received by editor(s): May 6, 2011
- Published electronically: March 19, 2012
- Additional Notes: The support from CNCSIS grant PN II-542/2009 of the Romanian Ministry of Education, Research and Innovation is gratefully acknowledged.
- Communicated by: Irena Peeva
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 3813-3822
- MSC (2010): Primary 13C15; Secondary 13F20, 05E40, 13F55, 05C25
- DOI: https://doi.org/10.1090/S0002-9939-2012-11371-1
- MathSciNet review: 2944722