Congruences on lattices (with application to amalgamation)

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dc.contributor.advisorRose, Henryen_ZA
dc.contributor.authorLaing, Lyneveen_ZA
dc.date.accessioned2016-03-04T16:34:18Z
dc.date.available2016-03-04T16:34:18Z
dc.date.issued1996en_ZA
dc.descriptionBibliography: pages 124-128.en_ZA
dc.description.abstractWe 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.en_ZA
dc.identifier.apacitationLaing, L. (1996). <i>Congruences on lattices (with application to amalgamation)</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17442en_ZA
dc.identifier.chicagocitationLaing, Lyneve. <i>"Congruences on lattices (with application to amalgamation)."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1996. http://hdl.handle.net/11427/17442en_ZA
dc.identifier.citationLaing, L. 1996. Congruences on lattices (with application to amalgamation). University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Laing, Lyneve AB - 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. DA - 1996 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1996 T1 - Congruences on lattices (with application to amalgamation) TI - Congruences on lattices (with application to amalgamation) UR - http://hdl.handle.net/11427/17442 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17442
dc.identifier.vancouvercitationLaing L. Congruences on lattices (with application to amalgamation). [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1996 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17442en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleCongruences on lattices (with application to amalgamation)en_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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