{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1033"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1033","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Standard Closure Operations on Several Rings of Dimension One","abstract":"There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the non-domain setting. Epstein has shown a correspondence between the set of finite-type semistar operations of a ring and the finite-type standard closures of a ring. I will classify the set of finite-type standard closures on several rings of dimension one.","abstract_html":"There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the non-domain setting. Epstein has shown a correspondence between the set of finite-type semistar operations of a ring and the finite-type standard closures of a ring. I will classify the set of finite-type standard closures on several rings of dimension one.","abstract_has_math":false,"creators":["Morre, Gregory"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Vassilev, Janet","Janet Vassilev","Alexandru Buium","James Degnan","Lance Miller"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-25T07:00:00Z","date_published":"2016-08-25T07:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["closure operation","standard","semistar","weakly prime","commutative ring"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/34"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/34","href":"https://digitalrepository.unm.edu/math_etds/34","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/33044","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Vassilev, Janet","Janet Vassilev","Alexandru Buium","James Degnan","Lance Miller"]},{"key":"dc:creator","label":"Author","values":["Morre, Gregory"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral","Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["closure operation","standard","semistar","weakly prime","commutative ring"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/33044","https://digitalrepository.unm.edu/math_etds/34"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the non-domain setting. Epstein has shown a correspondence between the set of finite-type semistar operations of a ring and the finite-type standard closures of a ring. I will classify the set of finite-type standard closures on several rings of dimension one."]},{"key":"dc:title","label":"Title","values":["Standard Closure Operations on Several Rings of Dimension One"]}]}],"canonical_facts":{"dc:contributor":["Vassilev, Janet","Janet Vassilev","Alexandru Buium","James Degnan","Lance Miller"],"dc:creator":["Morre, Gregory"],"dc:description.abstract":["There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the non-domain setting. Epstein has shown a correspondence between the set of finite-type semistar operations of a ring and the finite-type standard closures of a ring. I will classify the set of finite-type standard closures on several rings of dimension one."],"dc:identifier":["http://hdl.handle.net/1928/33044","https://digitalrepository.unm.edu/math_etds/34"],"dc:language":["English"],"dc:subject":["closure operation","standard","semistar","weakly prime","commutative ring"],"dc:title":["Standard Closure Operations on Several Rings of Dimension One"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}