Orderings of Monomial Ideals
Logic
2007-05-23 v1 Commutative Algebra
Combinatorics
Abstract
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute upper and lower bounds on the maximal order type.
Cite
@article{arxiv.math/0305384,
title = {Orderings of Monomial Ideals},
author = {Matthias Aschenbrenner and Wai-Yan Pong},
journal= {arXiv preprint arXiv:math/0305384},
year = {2007}
}
Comments
40 pages