Noncommutative Complete Isolated Singularities

Commutative local isolated singularities are a class of rings that have been studied extensively. Much work has been devoted in the area of noncommutative algebra in generalizing the notion of an isolated singularity for graded rings. However, one maintains a desire to directly adapt the notion of a Commutative local isolated singularity to the noncommutative case. We present some motivating theory in chapter 2 building to the definition and some extended theory of graded isolated singularities in chapter 3. In chapter 4 we build theory around ring completions allowing us to pass results about a connected graded isolated singularity $A$, to it's completion R=\hat{A}_\mA, which will necessarily be local. Finally, in chapter 5 we are able to use the ideas of previous chapters to prove the existence of Auslander-Reiten sequences for a well chosen category of modules over $R$.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2015

Author dc:creator

• Lyle, Justin Lee

• Algebra

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/57180

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/57180