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

 

Depth of factors of square free monomial ideals


Author: Dorin Popescu
Journal: Proc. Amer. Math. Soc. 142 (2014), 1965-1972
MSC (2010): Primary 13C15; Secondary 13F20, 13F55, 13P10
Published electronically: March 11, 2014
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Abstract: Let $ I$ be an ideal of a polynomial algebra over a field generated by $ r$ square free monomials of degree $ d$. If $ r$ is bigger than (or equal to, if $ I$ is not principal) the number of square free monomials of $ I$ of degree $ d+1$, then $ \mathrm {depth}_SI= d$. Let $ J\subsetneq I$, $ J\not =0$ be generated by square free monomials of degree $ \geq d+1$. If $ r$ is bigger than the number of square free monomials of $ I\setminus J$ of degree $ d+1$ or, more generally, the Stanley depth of $ I/J$ is $ d$, then $ \mathrm {depth}_SI/J= d$. In particular, Stanley's Conjecture holds in these cases.


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Additional Information

Dorin Popescu
Affiliation: Simion Stoilow Institute of Mathematics of Romanian Academy, Research Unit 5, P.O. Box 1-764, Bucharest 014700, Romania
Email: dorin.popescu@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11939-3
PII: S 0002-9939(2014)11939-3
Keywords: Monomial ideals, depth, Stanley depth
Received by editor(s): June 3, 2012
Received by editor(s) in revised form: July 12, 2012
Published electronically: March 11, 2014
Additional Notes: The author’s support from grant ID-PCE-2011-1023 of the Romanian Ministry of Education, Research and Innovation is gratefully acknowledged.
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.