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Congruences and amalgamation in small lattice varieties
Bibliography: pages 108-110.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613307292090368 |
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| access_status_str | Open Access |
| author | Ouwehand, Peter |
| author2 | Rose, Henry |
| author_browse | Ouwehand, Peter Rose, Henry |
| author_facet | Rose, Henry Ouwehand, Peter |
| author_sort | Ouwehand, Peter |
| collection | Thesis |
| description | Bibliography: pages 108-110. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/9054 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:03.682Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/9054 Congruences and amalgamation in small lattice varieties Ouwehand, Peter Rose, Henry Mathematics and Applied Mathematics Bibliography: pages 108-110. 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. 2014-11-04T08:43:36Z 2014-11-04T08:43:36Z 1998 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/9054 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Ouwehand, Peter Congruences and amalgamation in small lattice varieties |
| thesis_degree_str | Doctoral |
| title | Congruences and amalgamation in small lattice varieties |
| title_full | Congruences and amalgamation in small lattice varieties |
| title_fullStr | Congruences and amalgamation in small lattice varieties |
| title_full_unstemmed | Congruences and amalgamation in small lattice varieties |
| title_short | Congruences and amalgamation in small lattice varieties |
| title_sort | congruences and amalgamation in small lattice varieties |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/9054 |
| work_keys_str_mv | AT ouwehandpeter congruencesandamalgamationinsmalllatticevarieties |