Orderings of monomial ideals

• Autorzy: Matthias Aschenbrenner , Wai Yan Pong
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincar\'e series
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)
• 06A06: Partial order, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 1
• Strony: 27-74

Daty

wydano

2004

Twórcy

autor

Matthias Aschenbrenner

• Department of Mathematics, University of California at Berkeley, Evans Hall, Berkeley, CA 94720, U.S.A.

autor

Wai Yan Pong

• Department of Mathematics, California State University Dominguez-Hills, 1000 E. Victoria Street, Carson, CA 90747, U.S.A.

Identyfikatory

DOI

10.4064/fm181-1-2