{"id":{"repo_id":"mo-state","oai_identifier":"oai:bearworks.missouristate.edu:theses-1856"},"canonical_url":"https://search.dev.ndltd.org/etd/mo-state/oai:bearworks.missouristate.edu:theses-1856","repository":{"repo_id":"mo-state","name":"Missouri State University","base_url":"https://bearworks.missouristate.edu/do/oai/"},"display":{"title":"Application of the Tor Functor on Commutative R-Modules","abstract":"R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An element a∈A is a torsion element of a module A if there is a nonzerodivisor r∈R such that ra=0. For an arbitrary ring R if we take Q to be the localization of R with respect to the set of nonzerodivisors then we can show for any R-module A the module TorR₁(A, Q/R) is isomorphic to t(A), the torsion submodule of A. Furthermore, if A and B are arbitrary R-modules then in the case where R is a domain we have that TorRn(A, B) is torsion for all n≥1.","abstract_html":"R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An element a∈A is a torsion element of a module A if there is a nonzerodivisor r∈R such that ra=0. For an arbitrary ring R if we take Q to be the localization of R with respect to the set of nonzerodivisors then we can show for any R-module A the module TorR₁(A, Q/R) is isomorphic to t(A), the torsion submodule of A. Furthermore, if A and B are arbitrary R-modules then in the case where R is a domain we have that TorRn(A, B) is torsion for all n≥1.","abstract_has_math":false,"creators":["Lathrom, Grant"],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Cameron Wickham"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1998,"date_issued":"1998-07-01T07:00:00Z","date_published":"1998-07-01T07:00:00Z","updated_at":"2026-07-24T03:15:54Z","subjects":["Mathematics"],"languages":[],"rights":["© Grant Lathrom"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bearworks.missouristate.edu/theses/855","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cameron Wickham"]},{"key":"dc:creator","label":"Author","values":["Lathrom, Grant"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© Grant Lathrom"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://bearworks.missouristate.edu/theses/855"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An element a∈A is a torsion element of a module A if there is a nonzerodivisor r∈R such that ra=0. For an arbitrary ring R if we take Q to be the localization of R with respect to the set of nonzerodivisors then we can show for any R-module A the module TorR₁(A, Q/R) is isomorphic to t(A), the torsion submodule of A. Furthermore, if A and B are arbitrary R-modules then in the case where R is a domain we have that TorRn(A, B) is torsion for all n≥1."]},{"key":"dc:title","label":"Title","values":["Application of the Tor Functor on Commutative R-Modules"]}]}],"canonical_facts":{"dc:contributor":["Cameron Wickham"],"dc:creator":["Lathrom, Grant"],"dc:description.abstract":["R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An element a∈A is a torsion element of a module A if there is a nonzerodivisor r∈R such that ra=0. For an arbitrary ring R if we take Q to be the localization of R with respect to the set of nonzerodivisors then we can show for any R-module A the module TorR₁(A, Q/R) is isomorphic to t(A), the torsion submodule of A. Furthermore, if A and B are arbitrary R-modules then in the case where R is a domain we have that TorRn(A, B) is torsion for all n≥1."],"dc:identifier":["https://bearworks.missouristate.edu/theses/855"],"dc:rights":["© Grant Lathrom"],"dc:subject":["Mathematics"],"dc:title":["Application of the Tor Functor on Commutative R-Modules"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T03:15:54Z"}