The Library
Antichains of monomial ideals are finite
Tools
Tools
Tools
Maclagan, Diane. (2001) Antichains of monomial ideals are finite. American Mathematical Society. Proceedings, Vol.129 (No.6). pp. 1609-1615. ISSN 0002-9939
![[img]](http://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP_Maclagan_Antichains.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (139Kb) |
|
PDF
WRAP_Maclagan_Antichains.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (139Kb) |
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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of 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 |
| Date: | 2001 |
| Volume: | Vol.129 |
| Number: | No.6 |
| Page Range: | pp. 1609-1615 |
| Identification Number: | 10.1090/S0002-9939-00-05816-0 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | [1] William W. Adams, Serkan Hoşten, Philippe Loustaunau, and J. Lyn Miller. SAGBI and SAGBI-Gröbner bases over principal ideal domains. J. Symbolic Comput., 27:31{47, 1999. MR 99j:13023 [2] David Bayer and Ian Morrison. Standard bases and geometric invariant theory. I. Initial ideals and state polytopes. J. Symbolic Comput., 6(2-3):209{217, 1988. Computational aspects of commutative algebra. MR 90e:13001 [3] D. Duffus, M. Pouzet, and I. Rival. Complete ordered sets with no infinite antichains. Discrete Math., 35:39{52, 1981. MR 82j:06003 [4] Jonathan D. Farley, 1998. Private communication. [5] Teo Mora and Lorenzo Robbiano. The Gröbner fan of an ideal. J. Symbolic Comput., 6(2- 3):183{208, 1988. Computational aspects of commutative algebra. MR 90d:13004 [6] Tadao Oda. Problems on Minkowski sums of convex lattice polytopes. Preprint. 7 pages. [7] Bernd Sturmfels. Gröbner Bases and Convex Polytopes. American Mathematical Society, Providence, RI, 1996. MR 97b:13034 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/4294 |
Actions (login required)
 |
View Item |
