Geodesic
Orderings of monomial ideals
Matthias Aschenbrenner 1   ; Wai Yan Pong 2
1 Department of Mathematics University of California at Berkeley Evans Hall Berkeley, CA 94720, U.S.A.
2 Department of Mathematics California State University Dominguez-Hills 1000 E. Victoria Street Carson, CA 90747, U.S.A.
Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 27-74 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 bounds on the maximal order type.
DOI : 10.4064/fm181-1-2
Keywords: study set monomial ideals polynomial ring ordered set ordering given reverse inclusion short proof every antichain monomial ideals finite investigate ordinal invariants complexity ordered set particular interpretation height function terms hilbert samuel polynomial compute bounds maximal order type

Matthias Aschenbrenner  1   ; Wai Yan Pong  2

1 Department of Mathematics University of California at Berkeley Evans Hall Berkeley, CA 94720, U.S.A.
2 Department of Mathematics California State University Dominguez-Hills 1000 E. Victoria Street Carson, CA 90747, U.S.A. 
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Matthias Aschenbrenner; Wai Yan Pong. Orderings of monomial ideals. Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 27-74. doi: 10.4064/fm181-1-2

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