{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/90719"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/90719","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"The Golod Property on Monomial Rings","abstract":"In this paper, we work towards understanding a counterexample found in Lukas Katthan's \"A non-Golod Ring with a Trivial Product on its Koszul Homology\". In this counterexample, Katthan disproved a claim made by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this statement to be true.","abstract_html":"In this paper, we work towards understanding a counterexample found in Lukas Katthan's "A non-Golod Ring with a Trivial Product on its Koszul Homology". In this counterexample, Katthan disproved a claim made by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this statement to be true.","abstract_has_math":false,"creators":["Gilbert, Cody"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-27T22:02:17Z","subjects":["Algebraic Topology"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/90719","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gilbert, Cody"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-05-24T08:36:06Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-05-24T08:36:06Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Topology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/90719"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we work towards understanding a counterexample found in Lukas Katthan's \"A non-Golod Ring with a Trivial Product on its Koszul Homology\". In this counterexample, Katthan disproved a claim made by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this statement to be true."]},{"key":"dc:title","label":"Title","values":["The Golod Property on Monomial Rings"]}]}],"canonical_facts":{"dc:creator":["Gilbert, Cody"],"dc:date.accessioned":["2018-05-24T08:36:06Z"],"dc:date.available":["2018-05-24T08:36:06Z"],"dc:date.issued":["2018"],"dc:description.abstract":["In this paper, we work towards understanding a counterexample found in Lukas Katthan's \"A non-Golod Ring with a Trivial Product on its Koszul Homology\". In this counterexample, Katthan disproved a claim made by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this statement to be true."],"dc:identifier.uri":["http://hdl.handle.net/10339/90719"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Algebraic Topology"],"dc:title":["The Golod Property on Monomial Rings"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:17Z"}