On the relation type of systems of parameters and on the Poincare series of systems of parameters
Abstract
This thesis contains two different topics of commutative algebra, whose titles are joined together to form the title of the thesis. In chapter 1, we study the relation type of system of parameters. Let (R, m) be a commutative noetherian local ring of dimension d. Under some extra minor assumptions about the ring R, we investigate the difference between the relation type of one system of parameters and that of another. The results we obtain show the connection between the existence of the uniform bound for relation type of systems of parameters and the strong uniform Artin-Rees property and partially answer a question raised by C. Huneke. In chapter 2, we study the Poincare series of system of parameters. Let (R, m) be a commutative noetherian local ring of dimension two. We investigate the difference between the Poincare series of one system of parameters and that of another. The results we obtain show that if the ring (R, m) has finite local cohomology then there exists an "universal Poincare series" such that for any system of parameters $x\sb{1},\ x\sb{2}$, the Poincare series of the systems of parameters $x\sbsp{1}{n},\ x\sbsp{2}{n}$ converge to that "universal Poincare series".
Degree
Ph.D.
Advisors
Huneke, Purdue University.
Subject Area
Mathematics
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