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.
DOI
https://doi.org/10.57709/1059725
Recommended Citation
Baig, Muslim, "Primary Decomposition and Secondary Representation of Modules over a Commutative Ring." Thesis, Georgia State University, 2009.
doi: https://doi.org/10.57709/1059725