Title page for ETD etd-12012010-104308


Type of Document Dissertation
Author Cone, Randall Edward
Author's Email Address rcone@vt.edu
URN etd-12012010-104308
Title Finite Generation of Ext-Algebras for Monomial Algebras
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Green, Edward L. Committee Chair
Brown, Ezra A. Committee Member
Day, Martin V. Committee Member
Linnell, Peter A. Committee Member
Loehr, Nicholas A. Committee Member
Keywords
  • finite generation
  • cohomology
  • monomial algebras
Date of Defense 2010-11-30
Availability unrestricted
Abstract
The use of graphs in algebraic studies is ubiquitous, whether the graphs be finite or infinite, directed or undirected. Green and Zacharia have characterized finite generation of the cohomology rings of monomial algebras, and thereafter G. Davis determined a finite criteria for such generation in the case of cycle algebras. Herein, we describe the construction of a finite directed graph upon which criteria can be established to determine finite generation of the cohomology ring of in-spoked cycle" algebras, a class of algebras that includes cycle algebras. We then show the further usefulness of this constructed graph by studying other monomial algebras, including d-Koszul monomial algebras and a new class of monomial algebras which we term "left/right-symmetric" algebras.
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