Date of Award
7-18-2008
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Dr. Florian Enescu - Chair
Second Advisor
Dr. Frank Hall
Third Advisor
Dr. Yongwei Yao
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.
DOI
https://doi.org/10.57709/1059711
Recommended Citation
Malec, Sara, "Noetherian Filtrations and Finite Intersection Algebras." Thesis, Georgia State University, 2008.
doi: https://doi.org/10.57709/1059711