In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.
","abstract_html":"<p>In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.</p>","abstract_has_math":false,"creators":["Flinn, Erik"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Math and Computer Science","degree_department":null,"school":null,"contributors":["Daniel Rowe"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-05-01T07:00:00Z","date_published":"2021-05-01T07:00:00Z","updated_at":"2026-07-24T03:24:17Z","subjects":["Latin squares","quasigroups","loops","isotopy","nonassociative algebra","Lie groups","Lie quasigroups","Algebra","Set Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.nmu.edu/theses/654","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Daniel Rowe"]},{"key":"dc:creator","label":"Author","values":["Flinn, Erik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-04-02T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Math and Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Latin squares","quasigroups","loops","isotopy","nonassociative algebra","Lie groups","Lie quasigroups","Algebra","Set Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.nmu.edu/theses/654"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.
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"],"dc:identifier":["https://commons.nmu.edu/theses/654"],"dc:subject":["Latin squares","quasigroups","loops","isotopy","nonassociative algebra","Lie groups","Lie quasigroups","Algebra","Set Theory"],"dc:title":["Algebraic Structures and Variations: From Latin Squares to Lie Quasigroups"],"thesis:degree_discipline":["Math and Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T03:24:17Z"}