Orderings of monomial ideals

Matthias Aschenbrenner, and Wai Yan Pong. "Orderings of monomial ideals." Fundamenta Mathematicae 181.1 (2004): 27-74. <http://eudml.org/doc/283010>.

@article{MatthiasAschenbrenner2004,
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 bounds on the maximal order type.},
author = {Matthias Aschenbrenner, Wai Yan Pong},
journal = {Fundamenta Mathematicae},
keywords = {monomial ideals; polynomial ring; reverse inclusion; invariants; Noetherian ordered set; minimal order type; Hilbert-Samuel polynomials; graded -algebras; Hilbert polynomials},
language = {eng},
number = {1},
pages = {27-74},
title = {Orderings of monomial ideals},
url = {http://eudml.org/doc/283010},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Matthias Aschenbrenner
AU - Wai Yan Pong
TI - Orderings of monomial ideals
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 1
SP - 27
EP - 74
AB - 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.
LA - eng
KW - monomial ideals; polynomial ring; reverse inclusion; invariants; Noetherian ordered set; minimal order type; Hilbert-Samuel polynomials; graded -algebras; Hilbert polynomials
UR - http://eudml.org/doc/283010
ER -