Orderings of Monomial Ideals

2003/05/27 by Matthias Aschenbrenner, Aschenbrenner, Matthias, Wai-Yan Pong +1 · 1 citation
Mathematics · #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AC #math.CO #math.LO #msc:03E04 #msc:06A07 #msc:13D40

paper · pdf · doi:10.48550/arxiv.math/0305384

40 pages

arxiv created 2003/05/27 · arxiv updated 2009/11/30

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.

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• Proof-Theoretic Relations between Higman's and Kruskal's theorem, and Independence Results for Tree-like Structures

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