{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1673"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1673","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"On Gorenstein Projective and Gorenstein Flat Modules","abstract":"Purpose: H. Holm's metatheorem states, \"Every result in classical homological algebra has a counterpart in Gorenstein homological algebra\". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over such rings, a module M having finite Gorenstein at dimension is equivalent to M having finite Gorenstein projective dimension.","abstract_html":"Purpose: H. Holm's metatheorem states, "Every result in classical homological algebra has a counterpart in Gorenstein homological algebra". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over such rings, a module M having finite Gorenstein at dimension is equivalent to M having finite Gorenstein projective dimension.","abstract_has_math":false,"creators":["Smith, Chasen Grady"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["David R. Stone","Andrew V. Sills"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-12-01T08:00:00Z","date_published":"2011-12-01T08:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Module","Projective","Injective","Flat","Krull dimension","Noetherian","Gorenstein"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/673","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["David R. Stone","Andrew V. Sills"]},{"key":"dc:creator","label":"Author","values":["Smith, Chasen Grady"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Module","Projective","Injective","Flat","Krull dimension","Noetherian","Gorenstein"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/673"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Purpose: H. Holm's metatheorem states, \"Every result in classical homological algebra has a counterpart in Gorenstein homological algebra\". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over such rings, a module M having finite Gorenstein at dimension is equivalent to M having finite Gorenstein projective dimension."]},{"key":"dc:title","label":"Title","values":["On Gorenstein Projective and Gorenstein Flat Modules"]}]}],"canonical_facts":{"dc:contributor":["David R. Stone","Andrew V. Sills"],"dc:creator":["Smith, Chasen Grady"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["Purpose: H. Holm's metatheorem states, \"Every result in classical homological algebra has a counterpart in Gorenstein homological algebra\". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of a famous theorem of Gruson, Jensen, and Raynaud. Using this result we prove that over such rings, a module M having finite Gorenstein at dimension is equivalent to M having finite Gorenstein projective dimension."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/673"],"dc:subject":["ETD","Module","Projective","Injective","Flat","Krull dimension","Noetherian","Gorenstein"],"dc:title":["On Gorenstein Projective and Gorenstein Flat Modules"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}