{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/17442"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/17442","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Congruences on lattices (with application to amalgamation)","abstract":"We present some aspects of congruences on lattices. An overview of general results on congruence distributive algebras is given in Chapter 1 and in Chapter 2 we examine weak projections; including Dilworth's characterization of congruences on lattices and a finite basis theorem for lattices. The outstanding problem of whether congruence lattices of lattices characterize distributive algebraic lattices is discussed in Chapter 3 and we look at some of the partial results known to date. The last chapter (Chapter 6) characterizes the amalgamation class of a variety B generated by a B-lattice, B, as the intersection of sub direct products of B, 2-congruence extendible members of B and 2-chain limited members of B. To this end we consider 2-congruence extendibility in Chapter 4 and n-chain limited lattices in Chapter 5. Included in Chapter 4 is the result that in certain lattice varieties the amalgamation class is contained in the class of 2-congruence extendible members of the variety. A final theorem in Chapter 6 states that the amalgamation class of a B-lattice variety is a Horn class.","abstract_html":"We present some aspects of congruences on lattices. An overview of general results on congruence distributive algebras is given in Chapter 1 and in Chapter 2 we examine weak projections; including Dilworth's characterization of congruences on lattices and a finite basis theorem for lattices. The outstanding problem of whether congruence lattices of lattices characterize distributive algebraic lattices is discussed in Chapter 3 and we look at some of the partial results known to date. The last chapter (Chapter 6) characterizes the amalgamation class of a variety B generated by a B-lattice, B, as the intersection of sub direct products of B, 2-congruence extendible members of B and 2-chain limited members of B. To this end we consider 2-congruence extendibility in Chapter 4 and n-chain limited lattices in Chapter 5. Included in Chapter 4 is the result that in certain lattice varieties the amalgamation class is contained in the class of 2-congruence extendible members of the variety. A final theorem in Chapter 6 states that the amalgamation class of a B-lattice variety is a Horn class.","abstract_has_math":false,"creators":["Laing, Lyneve"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Rose, Henry"],"committee_chairs":[],"committee_members":[],"year":1996,"date_issued":"1996","date_published":"1996","updated_at":"2026-07-22T22:22:41Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/17442","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rose, Henry"]},{"key":"dc:creator","label":"Author","values":["Laing, Lyneve"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-03-04T16:34:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-03-04T16:34:18Z"]},{"key":"dc:date.issued","label":"Date","values":["1996"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/17442"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 124-128."]},{"key":"dc:description.abstract","label":"Abstract","values":["We present some aspects of congruences on lattices. An overview of general results on congruence distributive algebras is given in Chapter 1 and in Chapter 2 we examine weak projections; including Dilworth's characterization of congruences on lattices and a finite basis theorem for lattices. The outstanding problem of whether congruence lattices of lattices characterize distributive algebraic lattices is discussed in Chapter 3 and we look at some of the partial results known to date. The last chapter (Chapter 6) characterizes the amalgamation class of a variety B generated by a B-lattice, B, as the intersection of sub direct products of B, 2-congruence extendible members of B and 2-chain limited members of B. To this end we consider 2-congruence extendibility in Chapter 4 and n-chain limited lattices in Chapter 5. Included in Chapter 4 is the result that in certain lattice varieties the amalgamation class is contained in the class of 2-congruence extendible members of the variety. A final theorem in Chapter 6 states that the amalgamation class of a B-lattice variety is a Horn class."]},{"key":"dc:title","label":"Title","values":["Congruences on lattices (with application to amalgamation)"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rose, Henry"],"dc:creator":["Laing, Lyneve"],"dc:date.accessioned":["2016-03-04T16:34:18Z"],"dc:date.available":["2016-03-04T16:34:18Z"],"dc:date.issued":["1996"],"dc:description":["Bibliography: pages 124-128."],"dc:description.abstract":["We present some aspects of congruences on lattices. An overview of general results on congruence distributive algebras is given in Chapter 1 and in Chapter 2 we examine weak projections; including Dilworth's characterization of congruences on lattices and a finite basis theorem for lattices. The outstanding problem of whether congruence lattices of lattices characterize distributive algebraic lattices is discussed in Chapter 3 and we look at some of the partial results known to date. The last chapter (Chapter 6) characterizes the amalgamation class of a variety B generated by a B-lattice, B, as the intersection of sub direct products of B, 2-congruence extendible members of B and 2-chain limited members of B. To this end we consider 2-congruence extendibility in Chapter 4 and n-chain limited lattices in Chapter 5. Included in Chapter 4 is the result that in certain lattice varieties the amalgamation class is contained in the class of 2-congruence extendible members of the variety. A final theorem in Chapter 6 states that the amalgamation class of a B-lattice variety is a Horn class."],"dc:identifier.uri":["http://hdl.handle.net/11427/17442"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Congruences on lattices (with application to amalgamation)"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:41Z"}