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.
Recommended Citation
Morra, Todd Anthony, "An Introduction to Homological Algebra and its Applications" (2018). All Theses. 3001.
https://tigerprints.clemson.edu/all_theses/3001