Files in this item

FilesDescriptionFormat

application/pdf

application/pdf9971173.pdf (3MB)Restricted to U of Illinois
(no description provided)PDF

Description

Title:Monomial Ideals, N-Lists, and Smallest Graded Betti Numbers
Author(s):Richert, Benjamin P.
Doctoral Committee Chair(s):Evans, E. Graham, Jr.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:The second set of results in this thesis concerns the existence of smallest graded betti numbers. Given an Artinian Hilbert function H , consider all ideals I ⊂ R such that H(R/I) = H . Then the graded betti numbers which correspond to these ideals form a finite set which we partially order component-wise. It is known that this set has a largest element, but may fail to have a smallest element. This thesis extends, to an infinite family, the previous examples of Hilbert functions which fail to have a smallest element. Then we prove a conjecture of Geramita, Harima, and Shin which states that a smallest element need not exist when we restrict our inquiry to the graded betti numbers of Gorenstein ideals attaining H . Finally, we demonstrate with an infinite family that a smallest element may fail to exist even if H is the Hilbert function of an R-sequence.
Issue Date:2000
Type:Text
Language:English
Description:80 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.
URI:http://hdl.handle.net/2142/86997
Other Identifier(s):(MiAaPQ)AAI9971173
Date Available in IDEALS:2015-09-28
Date Deposited:2000


This item appears in the following Collection(s)

Item Statistics