Antichains of monomial ideals are finite (2001)
by
Diane Maclagan
| Venue: | Proc. Amer. Math. Soc |
| Citations: | 16 - 4 self |
BibTeX
@ARTICLE{Maclagan01antichainsof,
author = {Diane Maclagan},
title = {Antichains of monomial ideals are finite},
journal = {Proc. Amer. Math. Soc},
year = {2001},
volume = {129},
number = {6},
pages = {1609--1615}
}
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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 posets is shown to be false.
Citations
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| 63 | The Gröbner fan of an ideal - Mora, Robbiano - 1988 |
| 15 | Standard bases and geometric invariant theory - Bayer, Morrison - 1988 |
| 11 | Problems on Minkowski sums of convex lattice polytopes; arXiv:0812.1418 - Oda - 1997 |
| 6 | SAGBI and SAGBI-Gröbner bases over principal ideal domains - Adams, Ho¸sten, et al. - 1999 |
| 4 | Private communication - Bleak, Farley |
| 3 | Complete ordered sets with no infinite antichains - Duffus, Pouzet, et al. - 1981 |
