Antichains of monomial ideals are finite
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- by Diane Maclagan
- Proc. Amer. Math. Soc. 129 (2001), 1609-1615
- DOI: https://doi.org/10.1090/S0002-9939-00-05816-0
- Published electronically: October 31, 2000
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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.References
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Bibliographic 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
- MR Author ID: 607134
- Email: maclagan@math.berkeley.edu, maclagan@ias.edu
- Received by editor(s): September 15, 1999
- Published electronically: October 31, 2000
- Communicated by: Michael Stillman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1609-1615
- MSC (1991): Primary 13P10; Secondary 06A06, 52B20
- DOI: https://doi.org/10.1090/S0002-9939-00-05816-0
- MathSciNet review: 1814087