{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/29662"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/29662","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Quintic Abelian Fields","abstract":"Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed.","abstract_html":"Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed.","abstract_has_math":false,"creators":["Taylor, Frank Seaton"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Parry, Charles J."],"committee_members":["Floyd, William J.","Johnson, Lee W.","Brown, Ezra A.","Ball, Joseph A."],"year":1997,"date_issued":"1997-12-17","date_published":"1997-12-17","updated_at":"2026-07-22T22:20:07Z","subjects":["Abelian Fields","Class Number","Conductor","Fundamental Unit","Quintic Fields"],"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-111897-10412"],"render_values":[{"text":"etd-111897-10412","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/29662","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Parry, Charles J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Floyd, William J.","Johnson, Lee W.","Brown, Ezra A.","Ball, Joseph A."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Taylor, Frank Seaton"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:18:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:18:45Z","1998-12-22"]},{"key":"dc:date.issued","label":"Date","values":["1997-12-17"]},{"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. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Abelian Fields","Class Number","Conductor","Fundamental Unit","Quintic Fields"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-111897-10412"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/29662"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Quintic Abelian Fields"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Parry, Charles J."],"dc:contributor.committeemember":["Floyd, William J.","Johnson, Lee W.","Brown, Ezra A.","Ball, Joseph A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Taylor, Frank Seaton"],"dc:date.accessioned":["2014-03-14T20:18:45Z"],"dc:date.available":["2014-03-14T20:18:45Z","1998-12-22"],"dc:date.issued":["1997-12-17"],"dc:description.abstract":["Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed."],"dc:description.degree":["Ph. D."],"dc:identifier.other":["etd-111897-10412"],"dc:identifier.uri":["http://hdl.handle.net/10919/29662"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Abelian Fields","Class Number","Conductor","Fundamental Unit","Quintic Fields"],"dc:title":["Quintic Abelian Fields"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:07Z"}