Type of Document Master's Thesis Author Malec, Sara URN etd-07182008-132404 Title Noetherian Filtrations and Finite Intersection Algebras Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Florian Enescu Committee Chair Dr. Frank Hall Committee Member Dr. Yongwei Yao Committee Member Keywords
- intersection algebras
- E.P.F. filtrations
- Rees algebras
- Noetherian filtrations
- graded rings and modules
Date of Defense 2008-07-14 Availability unrestricted Abstract This paper presents the theory of Noetherian filtrations, an important concept in commutative algebra. The paper describes many aspects of the theory of these objects, presenting basic results, examples and applications. In the study of Noetherian filtrations, a few other important concepts are introduced such as Rees algebras, essential powers filtrations, and filtrations on modules. Basic results on these are presented as well. This thesis discusses at length how Noetherian filtrations relate to important constructions in commutative algebra, such as graded rings and modules, dimension theory and associated primes. In addition, the paper presents an original proof of the finiteness of the intersection algebra of principal ideals in a UFD. It concludes by discussing possible applications of this result to other areas of commutative algebra.Files
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