Graph and depth of a monomial squarefree ideal
Author:
Dorin Popescu
Journal:
Proc. Amer. Math. Soc. 140 (2012), 38133822
MSC (2010):
Primary 13C15; Secondary 13F20, 05E40, 13F55, 05C25
Published electronically:
March 19, 2012
MathSciNet review:
2944722
Fulltext PDF
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Abstract: Let be a monomial squarefree ideal of a polynomial ring over a field such that the sum of every three different ideals of its minimal prime ideals is the maximal ideal of , or more generally a constant ideal. We associate to a graph on , , on which we may read the depth of . In particular, does not depend on char . Also we show that satisfies Stanley's Conjecture.
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Additional Information
Dorin Popescu
Affiliation:
Institute of Mathematics “Simion Stoilow”, University of Bucharest, P.O. Box 1764, Bucharest 014700, Romania
Email:
dorin.popescu@imar.ro
DOI:
http://dx.doi.org/10.1090/S000299392012113711
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 II542/2009 of the Romanian Ministry of Education, Research and Innovation is gratefully acknowledged.
Communicated by:
Irena Peeva
Article copyright:
© Copyright 2012
American Mathematical Society
