{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/7654"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/7654","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Representations of McLain Groups","abstract":"Basic modules of McLain groups are defined and investigated. These are a (possibly infinite dimensional) generalization of Andre’s basic modules of the multiplicative group of upper triangular square matrices over a finite field with 1’s on the main diagonal. The ring R need not be finite or commutative and modules of a McLain group are allowed to be infinite dimensional over an arbitrary field F. The set , totally ordered by , is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and we study the problem of finding a decomposition of a basic module as direct sum of irreducible submodules.","abstract_html":"Basic modules of McLain groups are defined and investigated. These are a (possibly infinite dimensional) generalization of Andre’s basic modules of the multiplicative group of upper triangular square matrices over a finite field with 1’s on the main diagonal. The ring R need not be finite or commutative and modules of a McLain group are allowed to be infinite dimensional over an arbitrary field F. The set , totally ordered by , is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and we study the problem of finding a decomposition of a basic module as direct sum of irreducible submodules.","abstract_has_math":false,"creators":["Izadi, Mohammadali"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral -- first","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Szechtman, Fernando"],"committee_chairs":[],"committee_members":["Herman, Allen","Velez, Maria","Gilligan, Bruce"],"year":2016,"date_issued":"2016-06","date_published":"2016-06","updated_at":"2026-07-24T04:03:36Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4320"],"render_values":[{"text":"https://doi.org/10.82465/4320","href":"https://doi.org/10.82465/4320","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/7654","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Szechtman, Fernando"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Herman, Allen","Velez, Maria","Gilligan, Bruce"]},{"key":"dc:creator","label":"Author","values":["Izadi, Mohammadali"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-19T21:56:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-19T21:56:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-06"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral -- first"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"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.doi","label":"DOI","values":["https://doi.org/10.82465/4320"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/7654"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy In Mathematics, University of Regina. iv, 54 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["Basic modules of McLain groups are defined and investigated. These are a (possibly infinite dimensional) generalization of Andre’s basic modules of the multiplicative group of upper triangular square matrices over a finite field with 1’s on the main diagonal. The ring R need not be finite or commutative and modules of a McLain group are allowed to be infinite dimensional over an arbitrary field F. The set , totally ordered by , is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and we study the problem of finding a decomposition of a basic module as direct sum of irreducible submodules."]},{"key":"dc:title","label":"Title","values":["Representations of McLain Groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Szechtman, Fernando"],"dc:contributor.committeemember":["Herman, Allen","Velez, Maria","Gilligan, Bruce"],"dc:creator":["Izadi, Mohammadali"],"dc:date.accessioned":["2017-06-19T21:56:00Z"],"dc:date.available":["2017-06-19T21:56:00Z"],"dc:date.issued":["2016-06"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy In Mathematics, University of Regina. iv, 54 p."],"dc:description.abstract":["Basic modules of McLain groups are defined and investigated. These are a (possibly infinite dimensional) generalization of Andre’s basic modules of the multiplicative group of upper triangular square matrices over a finite field with 1’s on the main diagonal. The ring R need not be finite or commutative and modules of a McLain group are allowed to be infinite dimensional over an arbitrary field F. The set , totally ordered by , is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and we study the problem of finding a decomposition of a basic module as direct sum of irreducible submodules."],"dc:identifier.doi":["https://doi.org/10.82465/4320"],"dc:identifier.uri":["https://hdl.handle.net/10294/7654"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Representations of McLain Groups"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral -- first"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:36Z"}