{"id":{"repo_id":"gmu","oai_identifier":"oai:MARS:1920/8896"},"canonical_url":"https://search.dev.ndltd.org/etd/gmu/oai:MARS:1920/8896","repository":{"repo_id":"gmu","name":"George Mason University","base_url":"https://mars.gmu.edu/server/oai/request"},"display":{"title":"Ring Extensions Involving Amalgamated Duplications","abstract":"Within the last decade, much attention in commutative ring theory has been drawn into the revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known simply as a “bowtie ring.” The basic bowtie ring construction has roots as early as 1932, while the updated form simultaneously generalizes myriad other known constructions, including D + M rings, A + B rings, the rings A + B[X] and A + B[[X]] (for an extension ring B of the ring A), and Nagata's idealization of a module, a concept which itself has been indispensable in commutative algebra for over 50 years in providing examples of non-domains with various desired properties.","abstract_html":"Within the last decade, much attention in commutative ring theory has been drawn into the revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known simply as a “bowtie ring.” The basic bowtie ring construction has roots as early as 1932, while the updated form simultaneously generalizes myriad other known constructions, including D + M rings, A + B rings, the rings A + B[X] and A + B[[X]] (for an extension ring B of the ring A), and Nagata's idealization of a module, a concept which itself has been indispensable in commutative algebra for over 50 years in providing examples of non-domains with various desired properties.","abstract_has_math":false,"creators":["Long, Timothy Scott"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05","date_published":"2014-05","updated_at":"2026-07-27T19:51:46Z","subjects":["Mathematics","Algebra","Amalgamated Duplication","Bowtie Ring","Epimorphism","Idealization","Ring Extension"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/8896"],"render_values":[{"text":"hdl:1920/8896","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2014-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Algebra","Amalgamated Duplication","Bowtie Ring","Epimorphism","Idealization","Ring Extension"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/8896"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Within the last decade, much attention in commutative ring theory has been drawn into the revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known simply as a “bowtie ring.” The basic bowtie ring construction has roots as early as 1932, while the updated form simultaneously generalizes myriad other known constructions, including D + M rings, A + B rings, the rings A + B[X] and A + B[[X]] (for an extension ring B of the ring A), and Nagata's idealization of a module, a concept which itself has been indispensable in commutative algebra for over 50 years in providing examples of non-domains with various desired properties."]},{"key":"dc:title","label":"Title","values":["Ring Extensions Involving Amalgamated Duplications"]}]}],"canonical_facts":{"dc:date.issued":["2014-05"],"dc:description.other":["Within the last decade, much attention in commutative ring theory has been drawn into the revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known simply as a “bowtie ring.” The basic bowtie ring construction has roots as early as 1932, while the updated form simultaneously generalizes myriad other known constructions, including D + M rings, A + B rings, the rings A + B[X] and A + B[[X]] (for an extension ring B of the ring A), and Nagata's idealization of a module, a concept which itself has been indispensable in commutative algebra for over 50 years in providing examples of non-domains with various desired properties."],"dc:identifier":["hdl:1920/8896"],"dc:subject":["Mathematics","Algebra","Amalgamated Duplication","Bowtie Ring","Epimorphism","Idealization","Ring Extension"],"dc:title":["Ring Extensions Involving Amalgamated Duplications"],"dc:type":["Dissertation"]},"updated_at":"2026-07-27T19:51:46Z"}