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# Noncommutative Complete Isolated Singularities

## Electronic Theses and Dissertations

### Item Details

abstract
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 $R=\hat{A}_{\m_A}$, 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 $R$.
subject
Algebra
Complete
Isolated
Noncommutative
Ring
Singularity
contributor
Kirkman, Ellen (committee chair)
Moore, William F (committee member)
Rouse, Jeremy (committee member)
date
2015-06-23T08:35:58Z (accessioned)
2015-06-23T08:35:58Z (available)
2015 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/57180 (uri)
language
en (iso)
publisher
Wake Forest University
title
Noncommutative Complete Isolated Singularities
type
Thesis