{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/11583"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/11583","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"Group automorphisms of incidence algebras.","abstract":"Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤).","abstract_html":"Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤).","abstract_has_math":false,"creators":["Rebrovich, Jack, 1994-"],"institution":"Baylor University.","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Herden, Daniel."],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-08","date_published":"2021-08","updated_at":"2026-07-24T01:07:58Z","subjects":["Incidence algebras.","Maximal abelian.","Normal subgroups."],"languages":["en"],"rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2104/11583","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Herden, Daniel."]},{"key":"dc:creator","label":"Author","values":["Rebrovich, Jack, 1994-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-10-08T13:43:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-10-08T13:43:53Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-08"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Baylor University."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Incidence algebras.","Maximal abelian.","Normal subgroups."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2104/11583"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤)."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Group automorphisms of incidence algebras."]}]}],"canonical_facts":{"dc:contributor.advisor":["Herden, Daniel."],"dc:creator":["Rebrovich, Jack, 1994-"],"dc:date.accessioned":["2021-10-08T13:43:53Z"],"dc:date.available":["2021-10-08T13:43:53Z"],"dc:date.issued":["2021-08"],"dc:description.abstract":["Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤)."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/11583"],"dc:language.iso":["en"],"dc:rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"dc:subject":["Incidence algebras.","Maximal abelian.","Normal subgroups."],"dc:title":["Group automorphisms of incidence algebras."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:07:58Z"}