Congruences and amalgamation in small lattice varieties

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dc.contributor.advisorRose, Henryen_ZA
dc.contributor.authorOuwehand, Peteren_ZA
dc.date.accessioned2014-11-04T08:43:36Z
dc.date.available2014-11-04T08:43:36Z
dc.date.issued1998en_ZA
dc.descriptionBibliography: pages 108-110.en_ZA
dc.description.abstractWhen it became apparent that many varieties of algebras do not satisfy the Amalgamation Property, George Grätzer introduced the concept of an amalgamation class of a variety . The bulk of this dissertation is concerned with the amalgamation classes of residually small lattice varieties, with an emphasis on lattice varieties that are finitely generated. Our main concern is whether the amalgamation classes of such varieties are elementary classes or not. Chapters 0 and 1 provide a more detailed guide and summary of new and known results to be found in this dissertation. Chapter 2 is concerned with a cofinal sub-class of the amalgamation class of a residually small lattice variety, namely the class of absolute retracts, and completely characterizes the absolute retracts of finitely generated lattice varieties. Chapter 3 explores the strong connection between amalgamation and congruence extension properties in residually small lattice varieties. In Chapter 4, we investigate the closure of the amalgamation class under finite products. Chapter 5 is concerned with the amalgamation class of the variety generated by the pentagon. We prove that this amalgamation class is not an elementary class, but that, surprisingly, the class of all bounded members of the amalgamation class is a finitely axiomatizable Horn class. Chapters 6 and 7 introduce two techniques for proving that the amalgamation class of a residually small lattice variety is not an elementary class, and we give many examples. Finally, in Chapter 8, we look at the amalgamation classes of some residually large varieties, namely those generated by a finite dimensional simple lattice.en_ZA
dc.identifier.apacitationOuwehand, P. (1998). <i>Congruences and amalgamation in small lattice varieties</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/9054en_ZA
dc.identifier.chicagocitationOuwehand, Peter. <i>"Congruences and amalgamation in small lattice varieties."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998. http://hdl.handle.net/11427/9054en_ZA
dc.identifier.citationOuwehand, P. 1998. Congruences and amalgamation in small lattice varieties. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ouwehand, Peter AB - When it became apparent that many varieties of algebras do not satisfy the Amalgamation Property, George Grätzer introduced the concept of an amalgamation class of a variety . The bulk of this dissertation is concerned with the amalgamation classes of residually small lattice varieties, with an emphasis on lattice varieties that are finitely generated. Our main concern is whether the amalgamation classes of such varieties are elementary classes or not. Chapters 0 and 1 provide a more detailed guide and summary of new and known results to be found in this dissertation. Chapter 2 is concerned with a cofinal sub-class of the amalgamation class of a residually small lattice variety, namely the class of absolute retracts, and completely characterizes the absolute retracts of finitely generated lattice varieties. Chapter 3 explores the strong connection between amalgamation and congruence extension properties in residually small lattice varieties. In Chapter 4, we investigate the closure of the amalgamation class under finite products. Chapter 5 is concerned with the amalgamation class of the variety generated by the pentagon. We prove that this amalgamation class is not an elementary class, but that, surprisingly, the class of all bounded members of the amalgamation class is a finitely axiomatizable Horn class. Chapters 6 and 7 introduce two techniques for proving that the amalgamation class of a residually small lattice variety is not an elementary class, and we give many examples. Finally, in Chapter 8, we look at the amalgamation classes of some residually large varieties, namely those generated by a finite dimensional simple lattice. DA - 1998 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1998 T1 - Congruences and amalgamation in small lattice varieties TI - Congruences and amalgamation in small lattice varieties UR - http://hdl.handle.net/11427/9054 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/9054
dc.identifier.vancouvercitationOuwehand P. Congruences and amalgamation in small lattice varieties. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9054en_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.otherMathematics and Applied Mathematicsen_ZA
dc.titleCongruences and amalgamation in small lattice varietiesen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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