Author

Muslim Baig

Date of Award

4-21-2009

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Florian Enescu - Chair

Second Advisor

Dr. Imre Patyi

Third Advisor

Dr. Yongwei Yao

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.

Included in

Mathematics Commons

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