{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/78130"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/78130","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Epsilon multiplicity for graded algebras","abstract":"[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. The purpose of our thesis is to show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning epsilon multiplicity, as corollaries of our main theorem.","abstract_html":"[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. The purpose of our thesis is to show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning epsilon multiplicity, as corollaries of our main theorem.","abstract_has_math":false,"creators":["Das, Suprajo"],"institution":"University of Missouri--Columbia","degree_name":"Ph. D.","degree_level":"Doctoral","degree_discipline":"Mathematics (MU)","degree_department":null,"school":null,"contributors":[],"advisors":["Cutkosky, Dale"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-24T03:08:20Z","subjects":[],"languages":["eng","English"],"rights":["Access to files is limited to the campuses of the University of Missouri with SSO login."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.32469/10355/78130"],"render_values":[{"text":"https://doi.org/10.32469/10355/78130","href":"https://doi.org/10.32469/10355/78130","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10355/78130","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Cutkosky, Dale"]},{"key":"dc:creator","label":"Author","values":["Das, Suprajo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-11-03T15:56:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-11-03T15:56:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:publisher","label":"Institution","values":["University of Missouri--Columbia"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (MU)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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It is important to know if it can be realized as a limit. The purpose of our thesis is to show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning epsilon multiplicity, as corollaries of our main theorem."]},{"key":"dc:title","label":"Title","values":["Epsilon multiplicity for graded algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Cutkosky, Dale"],"dc:creator":["Das, Suprajo"],"dc:date.accessioned":["2020-11-03T15:56:57Z"],"dc:date.available":["2020-11-03T15:56:57Z"],"dc:date.issued":["2020"],"dc:description.abstract":["[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. The purpose of our thesis is to show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning epsilon multiplicity, as corollaries of our main theorem."],"dc:identifier.doi":["https://doi.org/10.32469/10355/78130"],"dc:identifier.uri":["https://hdl.handle.net/10355/78130"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["Access to files is limited to the campuses of the University of Missouri with SSO login."],"dc:title":["Epsilon multiplicity for graded algebras"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:08:20Z"}