Date of Award
4-21-2010
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Yongwei Yao - Committee Chair
Second Advisor
Florian Enescu - Committee Member
Third Advisor
Imre Patyi - Committee Member
Abstract
This paper presents the theory of weak primary decomposition of modules over a commutative ring. A generalization of the classic well-known theory of primary decomposition, weak primary decomposition is a consequence of the notions of weakly associated prime ideals and nearly nilpotent elements, which were introduced by N. Bourbaki. We begin by discussing basic facts about classic primary decomposition. Then we prove the results on weak primary decomposition, which are parallel to the classic case. Lastly, we define and generalize the Compatibility property of primary decomposition.
DOI
https://doi.org/10.57709/1332032
Recommended Citation
Stalvey, Harrison, "Weak Primary Decomposition of Modules Over a Commutative Ring." Thesis, Georgia State University, 2010.
doi: https://doi.org/10.57709/1332032