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Noetherian Filtrations and Finite Intersection Algebras

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.

Identiferoai:union.ndltd.org:GEORGIA/oai:scholarworks.gsu.edu:math_theses-1054
Date18 July 2008
CreatorsMalec, Sara
PublisherScholarWorks @ Georgia State University
Source SetsGeorgia State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMathematics Theses

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