{"id":{"repo_id":"umkc","oai_identifier":"oai:mospace.umsystem.edu:10355/47457"},"canonical_url":"https://search.dev.ndltd.org/etd/umkc/oai:mospace.umsystem.edu:10355/47457","repository":{"repo_id":"umkc","name":"University of Missouri - Kansas City","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Generalized Koszul Properties of Commutative Local Rings","abstract":"We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2.","abstract_html":"We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2.","abstract_has_math":false,"creators":["Hoffmeier, Justin Cole"],"institution":null,"degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":"Mathematics (UMKC)","degree_department":null,"school":null,"contributors":[],"advisors":["Sega, Liana"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-24T05:18:49Z","subjects":[],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/47457","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sega, Liana"]},{"key":"dc:creator","label":"Author","values":["Hoffmeier, Justin Cole"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-12-09T14:31:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-12-09T14:31:54Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (UMKC)","Physics (UMKC)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/47457"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Title from PDF of title page, viewed on December 11, 2015","Dissertation advisor: Liana Sega","Vita","Includes bibliographical references (pages 48-51)","Thesis (Ph.D.)--Department of Mathematics and Statistics and Department of Physics and Astronomy. University of Missouri--Kansas City, 2014"]},{"key":"dc:description.abstract","label":"Abstract","values":["We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2."]},{"key":"dc:title","label":"Title","values":["Generalized Koszul Properties of Commutative Local Rings"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sega, Liana"],"dc:creator":["Hoffmeier, Justin Cole"],"dc:date.accessioned":["2015-12-09T14:31:54Z"],"dc:date.available":["2015-12-09T14:31:54Z"],"dc:date.issued":["2014"],"dc:description":["Title from PDF of title page, viewed on December 11, 2015","Dissertation advisor: Liana Sega","Vita","Includes bibliographical references (pages 48-51)","Thesis (Ph.D.)--Department of Mathematics and Statistics and Department of Physics and Astronomy. University of Missouri--Kansas City, 2014"],"dc:description.abstract":["We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2."],"dc:identifier.uri":["https://hdl.handle.net/10355/47457"],"dc:language.iso":["en_US"],"dc:title":["Generalized Koszul Properties of Commutative Local Rings"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (UMKC)","Physics (UMKC)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:18:49Z"}