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Congruences on lattices (with application to amalgamation)
Bibliography: pages 124-128.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613172364476416 |
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| access_status_str | Open Access |
| author | Laing, Lyneve |
| author2 | Rose, Henry |
| author_browse | Laing, Lyneve Rose, Henry |
| author_facet | Rose, Henry Laing, Lyneve |
| author_sort | Laing, Lyneve |
| collection | Thesis |
| description | Bibliography: pages 124-128. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17442 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:54.917Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| 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:11427/17442 Congruences on lattices (with application to amalgamation) Laing, Lyneve Rose, Henry Mathematics Bibliography: pages 124-128. 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. 2016-03-04T16:34:18Z 2016-03-04T16:34:18Z 1996 Master Thesis Masters MSc http://hdl.handle.net/11427/17442 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Laing, Lyneve Congruences on lattices (with application to amalgamation) |
| thesis_degree_str | Master's |
| title | Congruences on lattices (with application to amalgamation) |
| title_full | Congruences on lattices (with application to amalgamation) |
| title_fullStr | Congruences on lattices (with application to amalgamation) |
| title_full_unstemmed | Congruences on lattices (with application to amalgamation) |
| title_short | Congruences on lattices (with application to amalgamation) |
| title_sort | congruences on lattices with application to amalgamation |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17442 |
| work_keys_str_mv | AT lainglyneve congruencesonlatticeswithapplicationtoamalgamation |