 
Summary: Orderings of Monomial Ideals
Matthias Aschenbrenner
Department of Mathematics
University of California at Berkeley
Evans Hall
Berkeley, CA 94720
maschenb@math.berkeley.edu
Wai Yan Pong
Department of Mathematics
California State University DominguezHills
1000 E. Victoria Street
Carson, CA 90747
pong@math.csudh.edu
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 HilbertSamuel polynomial, and we compute
