Type of Document Master's Thesis Author Baig, Muslim URN etd-04202009-234258 Title Primary Decomposition and Secondary Representation of Modules over a Commutative Ring Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Florian Enescu Committee Chair Dr. Imre Patyi Committee Member Dr. Yongwei Yao Committee Member Keywords
- p-adic numbers
- Inverse limit
- Primary decomposition
- Associated primes
- Attached primes
- Secondary representation
Date of Defense 2009-04-15 Availability unrestricted Abstract This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particular, the existence of a secondary representation for Artinian modules. It concludes with some interesting examples of both secondary and representable modules, highlighting the consequences of the results thus established.Files
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