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oai:null:10339/571802026-09-18T14:12:58Zcom_10339_14934col_10339_38132

Lyle, Justin Lee 2015-06-23T08:35:58Z 2015-06-23T08:35:58Z 2015 https://wakespace.lib.wfu.edu/handle/10339/57180 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 $R$. en Wake Forest University Algebra Complete Isolated Noncommutative Ring Singularity Noncommutative Complete Isolated Singularities Thesis Kirkman, Ellen Moore, William F Rouse, Jeremy Mathematics open.access