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Weak Primary Decomposition of Modules Over a Commutative Ring

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.

Identiferoai:union.ndltd.org:GEORGIA/oai:digitalarchive.gsu.edu:math_theses-1084
Date21 April 2010
CreatorsStalvey, Harrison
PublisherDigital Archive @ GSU
Source SetsGeorgia State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMathematics Theses

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