{"id":{"repo_id":"csusb","oai_identifier":"oai:scholarworks.lib.csusb.edu:etd-1150"},"canonical_url":"https://search.dev.ndltd.org/etd/csusb/oai:scholarworks.lib.csusb.edu:etd-1150","repository":{"repo_id":"csusb","name":"CSUniversity San Bernardino","base_url":"https://scholarworks.lib.csusb.edu/do/oai/"},"display":{"title":"A Fundamental Unit of O_K","abstract":"<p>In the classical case we make use of Pells equation to compute units in the ring O<sub>F. </sub> Consider the parallel to the classical case and the quadratic field extension that creates the ring O<sub>K</sub>. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units. </p>","abstract_html":"&lt;p&gt;In the classical case we make use of Pells equation to compute units in the ring O&lt;sub&gt;F. &lt;/sub&gt; Consider the parallel to the classical case and the quadratic field extension that creates the ring O&lt;sub&gt;K&lt;/sub&gt;. We use the generalized Pell&#x27;s equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units. &lt;/p&gt;","abstract_has_math":false,"creators":["Munoz, Susana L"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["J. Paul Vicknair"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-03-01T08:00:00Z","date_published":"2015-03-01T08:00:00Z","updated_at":"2026-07-24T01:52:45Z","subjects":["Unit","Algebraic Extensions","Pells equation","continued fractions","Algebra","Number Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["J. Paul Vicknair"]},{"key":"dc:creator","label":"Author","values":["Munoz, Susana L"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-03-09T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Unit","Algebraic Extensions","Pells equation","continued fractions","Algebra","Number Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>In the classical case we make use of Pells equation to compute units in the ring O<sub>F. </sub> Consider the parallel to the classical case and the quadratic field extension that creates the ring O<sub>K</sub>. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units. </p>"]},{"key":"dc:title","label":"Title","values":["A Fundamental Unit of O_K"]}]}],"canonical_facts":{"dc:contributor":["J. Paul Vicknair"],"dc:creator":["Munoz, Susana L"],"dc:date.available":["2015-03-09T07:00:00Z"],"dc:description.abstract":["<p>In the classical case we make use of Pells equation to compute units in the ring O<sub>F. </sub> Consider the parallel to the classical case and the quadratic field extension that creates the ring O<sub>K</sub>. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units. </p>"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/133"],"dc:subject":["Unit","Algebraic Extensions","Pells equation","continued fractions","Algebra","Number Theory"],"dc:title":["A Fundamental Unit of O_K"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:45Z"}