Orderings of Monomial Ideals

Details Orderings of Monomial Ideals Orderings of Monomial Ideals

2003-05-27

arxiv.org/abs/math/0305384v1

Mathematics

Logic

40 pages

Scientific paper

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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