Orderings of monomial ideals

Tom 181 / 2004

Matthias Aschenbrenner, Wai Yan Pong Fundamenta Mathematicae 181 (2004), 27-74 MSC: Primary 06A06; Secondary 13D40, 13P10. DOI: 10.4064/fm181-1-2

Streszczenie

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.

Autorzy

  • Matthias AschenbrennerDepartment of Mathematics
    University of California at Berkeley
    Evans Hall
    Berkeley, CA 94720, U.S.A.
    e-mail
  • Wai Yan PongDepartment of Mathematics
    California State University Dominguez-Hills
    1000 E. Victoria Street
    Carson, CA 90747, U.S.A.
    e-mail

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