Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.

Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Hilbert-Samuel and Hilbert-Kunz functions of zero-dimensional ideals

Lori McDonnell, University of Nebraska - Lincoln

Abstract

The Hilbert-Samuel function measures the length of powers of a zero-dimensional ideal in a local ring. Samuel showed that over a local ring these lengths agree with a polynomial, called the Hilbert-Samuel polynomial, for sufficiently large powers of the ideal. We examine the coefficients of this polynomial in the case the ideal is generated by a system of parameters, focusing much of our attention on the second Hilbert coefficient. We also consider the Hilbert-Kunz function, which measures the length of Frobenius powers of an ideal in a ring of positive characteristic. In particular, we examine a conjecture of Watanabe and Yoshida comparing the Hilbert-Kunz multiplicity and the length of the ideal and provide a proof in the graded case. ^

Subject Area

Mathematics

Recommended Citation

McDonnell, Lori, "Hilbert-Samuel and Hilbert-Kunz functions of zero-dimensional ideals" (2011). ETD collection for University of Nebraska - Lincoln. AAI3450102.
http://digitalcommons.unl.edu/dissertations/AAI3450102

Share

COinS