{"id":{"repo_id":"umkc","oai_identifier":"oai:mospace.umsystem.edu:10355/101625"},"canonical_url":"https://search.dev.ndltd.org/etd/umkc/oai:mospace.umsystem.edu:10355/101625","repository":{"repo_id":"umkc","name":"University of Missouri - Kansas City","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"A study of homological invariants modulo an exact zero divisor","abstract":"Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series.","abstract_html":"Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series.","abstract_has_math":false,"creators":["Sireeshan, Deepak"],"institution":"University of Missouri--Kansas City","degree_name":"Ph.D. (Doctor of Philosophy)","degree_level":"Doctoral","degree_discipline":"Mathematics (UMKC)","degree_department":null,"school":null,"contributors":[],"advisors":["Sega, Liana","Uddin, Md Yusuf Sarwar (Mohammad Yusuf Sarwar)"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024","date_published":"2024","updated_at":"2026-07-24T05:16:44Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/101625","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sega, Liana","Uddin, Md Yusuf Sarwar (Mohammad Yusuf Sarwar)"]},{"key":"dc:creator","label":"Author","values":["Sireeshan, Deepak"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-06-03T16:05:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-06-03T16:05:16Z"]},{"key":"dc:date.issued","label":"Date","values":["2024"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (UMKC)","Computer Science (UMKC)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D. (Doctor of Philosophy)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Kansas City"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/101625"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Title from PDF of title page viewed June 6, 2024","Dissertation advisors: Liana Sega and Yusuf Uddin","Vita","Includes bibliographical references (pages 97-102)","Dissertation (Ph.D.)--Department of Mathematics and Statistics and School of Computing and Engineering. University of Missouri--Kansas City, 2024"]},{"key":"dc:description.abstract","label":"Abstract","values":["Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series."]},{"key":"dc:title","label":"Title","values":["A study of homological invariants modulo an exact zero divisor"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sega, Liana","Uddin, Md Yusuf Sarwar (Mohammad Yusuf Sarwar)"],"dc:creator":["Sireeshan, Deepak"],"dc:date.accessioned":["2024-06-03T16:05:16Z"],"dc:date.available":["2024-06-03T16:05:16Z"],"dc:date.issued":["2024"],"dc:description":["Title from PDF of title page viewed June 6, 2024","Dissertation advisors: Liana Sega and Yusuf Uddin","Vita","Includes bibliographical references (pages 97-102)","Dissertation (Ph.D.)--Department of Mathematics and Statistics and School of Computing and Engineering. University of Missouri--Kansas City, 2024"],"dc:description.abstract":["Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series."],"dc:identifier.uri":["https://hdl.handle.net/10355/101625"],"dc:title":["A study of homological invariants modulo an exact zero divisor"],"thesis:degree_discipline":["Mathematics (UMKC)","Computer Science (UMKC)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D. (Doctor of Philosophy)"],"thesis:institution_name":["University of Missouri--Kansas City"]},"updated_at":"2026-07-24T05:16:44Z"}