Finite Generation of Ext-Algebras for Monomial Algebras

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2010

Author dc:creator

• Cone, Randall Edward

Chair dc:contributor.committeechair

• Green, Edward L.

Committee members dc:contributor.committeemember

• Loehr, Nicholas A.
• Linnell, Peter A.
• Brown, Ezra A.
• Day, Martin V.

• finite generation
• cohomology
• monomial algebras

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-12012010-104308

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29865