{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/31161"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/31161","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"New examples of four dimensional AS-regular algebras","abstract":"This thesis deals with AS-regular algebras, first defined by Michael Artin and William Schelter in Graded Algebras of Global Dimension 3. All such algebras of dimension three have been classified, but the corresponding problem in higher dimensions remains open. We construct new examples of four dimensional AS-regular algebras, and provide some information about their module structure. Results are provided for proving the regularity of such algebras. In addition we classify the AS-regular algebras of dimension four satisfying certain conditions.","abstract_html":"This thesis deals with AS-regular algebras, first defined by Michael Artin and William Schelter in Graded Algebras of Global Dimension 3. All such algebras of dimension three have been classified, but the corresponding problem in higher dimensions remains open. We construct new examples of four dimensional AS-regular algebras, and provide some information about their module structure. Results are provided for proving the regularity of such algebras. In addition we classify the AS-regular algebras of dimension four satisfying certain conditions.","abstract_has_math":false,"creators":["Caines, Ian"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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All such algebras of dimension three have been classified, but the corresponding problem in higher dimensions remains open. We construct new examples of four dimensional AS-regular algebras, and provide some information about their module structure. Results are provided for proving the regularity of such algebras. In addition we classify the AS-regular algebras of dimension four satisfying certain conditions."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["New examples of four dimensional AS-regular algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Johan de Jong."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. 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In addition we classify the AS-regular algebras of dimension four satisfying certain conditions."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/31161"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["New examples of four dimensional AS-regular algebras"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:02Z"}