{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1670"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1670","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Gorenstein Injective Modules","abstract":"One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct sum of Gorenstein injective modules is still Gorenstein injective.","abstract_html":"One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct sum of Gorenstein injective modules is still Gorenstein injective.","abstract_has_math":false,"creators":["McLean, Emily"],"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":["Scott Kersey","Goran Lesaja"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-11-01T07:00:00Z","date_published":"2011-11-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Injective module","Gorenstein injective module"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/670","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Scott Kersey","Goran Lesaja"]},{"key":"dc:creator","label":"Author","values":["McLean, Emily"]}]},{"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","Injective module","Gorenstein injective module"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/670"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct sum of Gorenstein injective modules is still Gorenstein injective."]},{"key":"dc:title","label":"Title","values":["Gorenstein Injective Modules"]}]}],"canonical_facts":{"dc:contributor":["Scott Kersey","Goran Lesaja"],"dc:creator":["McLean, Emily"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct sum of Gorenstein injective modules is still Gorenstein injective."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/670"],"dc:subject":["ETD","Injective module","Gorenstein injective module"],"dc:title":["Gorenstein Injective 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"}