{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/29865"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/29865","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Finite Generation of Ext-Algebras for Monomial Algebras","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Cone, Randall Edward"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Green, Edward L."],"committee_members":["Loehr, Nicholas A.","Linnell, Peter A.","Brown, Ezra A.","Day, Martin V."],"year":2010,"date_issued":"2010-11-30","date_published":"2010-11-30","updated_at":"2026-07-22T22:19:29Z","subjects":["finite generation","cohomology","monomial algebras"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12012010-104308"],"render_values":[{"text":"etd-12012010-104308","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/29865","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Green, Edward L."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Loehr, Nicholas A.","Linnell, Peter A.","Brown, Ezra A.","Day, Martin V."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Cone, Randall Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:19:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:19:36Z","2010-12-09"]},{"key":"dc:date.issued","label":"Date","values":["2010-11-30"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Finite Generation of Ext-Algebras for Monomial Algebras"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Green, Edward L."],"dc:contributor.committeemember":["Loehr, Nicholas A.","Linnell, Peter A.","Brown, Ezra A.","Day, Martin V."],"dc:contributor.department":["Mathematics"],"dc:creator":["Cone, Randall Edward"],"dc:date.accessioned":["2014-03-14T20:19:36Z"],"dc:date.available":["2014-03-14T20:19:36Z","2010-12-09"],"dc:date.issued":["2010-11-30"],"dc:description.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."],"dc:description.degree":["Ph. D."],"dc:identifier.other":["etd-12012010-104308"],"dc:identifier.uri":["http://hdl.handle.net/10919/29865"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["finite generation","cohomology","monomial algebras"],"dc:title":["Finite Generation of Ext-Algebras for Monomial Algebras"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. 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