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Antichains of monomial ideals are finite
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Maclagan, Diane (2001) Antichains of monomial ideals are finite. American Mathematical Society. Proceedings, Vol.129 (No.6). pp. 1609-1615. doi:10.1090/S0002-9939-00-05816-0 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-00-05816-0
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Partially ordered sets, Polynomial rings | ||||
Journal or Publication Title: | American Mathematical Society. Proceedings | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9939 | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | Vol.129 | ||||
Number: | No.6 | ||||
Page Range: | pp. 1609-1615 | ||||
DOI: | 10.1090/S0002-9939-00-05816-0 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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