Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Yongwei Yao - Committee Chair

Second Advisor

Florian Enescu - Committee Member

Third Advisor

Imre Patyi - Committee Member


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.

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