Mathematics, Department of
Department of Mathematics: Dissertations, Theses, and Student Research
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
First Advisor
Srikanth B. Iyengar
Date of this Version
Spring 4-12-2013
Document Type
Dissertation
Abstract
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t,t^{-1}] associated to R. This module, denoted (R), is the free Z[t,t^{-1}]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The main result is a structure theorem for J(R) when R is a complete Gorenstein local ring; the link between periodicity and torsion stated above is a corollary.
Advisor: Srikanth Iyengar
Comments
A dissertation Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Srikanth Iyengar. Lincoln, Nebraska: May, 2013
Copyright (c) 2013 Amanda Croll