Hilbert-Samuel polynomials and building indecomposable modules
by Crabbe, Andrew, Ph.D., THE UNIVERSITY OF NEBRASKA - LINCOLN, 2008, 43 pages; 3315330

Abstract:

Let (R, [special characters omitted], k) be a Noetherian local ring and M and N be finitely generated. In this thesis, we give precise formulas for the generalized Hilbert-Samuel polynomials associated to the torsion and contravariant extension functors, that is, polynomials giving the lengths of the modules [special characters omitted] and [special characters omitted], respectively. One application of these results is that they can be used to give information about the dimensions of syzygies of finite length modules.

We also show this if R is complete and has depth at least 2, then one can build indecomposable modules of arbitrarily prescribed constant rank. Moreover, if R is assumed to be Cohen-Macaulay, then these modules can be chosen to be maximal Cohen-Macaulay when localized on the punctured spectrum.

 
AdviserRoger Wiegand
SchoolTHE UNIVERSITY OF NEBRASKA - LINCOLN
SourceDAI/B 69-07, p. , Oct 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3315330
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