Graded Betti Numbers and Hilbert Functions of Graded Cohen-Macaulay Modules
| Autor: | Söderberg, Jonas |
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| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: | |
| Druh dokumentu: | Doctoral Thesis<br />Text |
| Popis: | In this thesis we study graded Cohen-Macaulay modules and their possible Hilbert functions and graded Betti numbers. In most cases the Cohen-Macaulay modules we study are level modules. In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain level modules. As in the case of level algebras, a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences. We prove that a sequence of positive integers (h0, h1, ..., hc) is the Hilbert function of an artinian level module of codimension two if and only if hi−1 − 2hi + hi+1 QC 20100819 |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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