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

 

Antichains of monomial ideals are finite


Author: Diane Maclagan
Journal: Proc. Amer. Math. Soc. 129 (2001), 1609-1615
MSC (1991): Primary 13P10; Secondary 06A06, 52B20
Published electronically: October 31, 2000
MathSciNet review: 1814087
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Abstract:

The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the literature and new results. One natural generalization to more abstract posets is shown to be false.


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Additional Information

Diane Maclagan
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
Email: maclagan@math.berkeley.edu, maclagan@ias.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05816-0
PII: S 0002-9939(00)05816-0
Keywords: Posets, monomial ideal, Gr\"obner bases
Received by editor(s): September 15, 1999
Published electronically: October 31, 2000
Communicated by: Michael Stillman
Article copyright: © Copyright 2000 American Mathematical Society