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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Graph and depth of a monomial squarefree ideal


Author: Dorin Popescu
Journal: Proc. Amer. Math. Soc. 140 (2012), 3813-3822
MSC (2010): Primary 13C15; Secondary 13F20, 05E40, 13F55, 05C25
Published electronically: March 19, 2012
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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=\vert\operatorname {Min}S/I\vert$, 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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11371-1
PII: S 0002-9939(2012)11371-1
Keywords: Monomial ideals, join graphs, size, depth, Stanley depth
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
Article copyright: © Copyright 2012 American Mathematical Society