Date of Award

12-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Committee Member

Dr. Sean Sather-Wagstaff, Committee Chair

Committee Member

Dr. James Coykendall

Committee Member

Dr. Felice Manganiello

Abstract

Ext modules have a number of applications in homological algebra and commutative abstract algebra as a whole. In this document we prove Ext modules are well-defined and motivate their study by characterizing the depth of a ring in terms of Ext modules as well as by giving an application in combinatorial commutative algebra. In particular, we give a way of constructing Cohen-Macaulay rings from simple graphs and show that when we localize these rings, their type is easily computed by counting the number of maximal cliques in the appropriate simple graph. When R is a noetherian ring and S the local ring resulting from localizing R at one of its prime ideals, it has been shown that there is a well-defined map from the set of isomorphism classes of semidualizing modules of R to the set of isomorphism classes of semidualizing modules of S. We use the same ring construction mentioned above to show this map need not be surjective.

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