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Varieties of lattices
Bibliography: pages 140-145.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613316289921024 |
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| access_status_str | Open Access |
| author | Jipsen, Peter |
| author2 | Rose, Henry |
| author_browse | Jipsen, Peter Rose, Henry |
| author_facet | Rose, Henry Jipsen, Peter |
| author_sort | Jipsen, Peter |
| collection | Thesis |
| description | Bibliography: pages 140-145. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15851 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:10.861Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| 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:11427/15851 Varieties of lattices Jipsen, Peter Rose, Henry Lattice theory Bibliography: pages 140-145. An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of information has been obtained in the last twenty years. We begin with some preliminary results from universal algebra and lattice theory. The next chapter presents some properties of the lattice of all lattice sub-varieties. Here we also discuss the important notion of a splitting pair of varieties and give several characterisations of the associated splitting lattice. The more detailed study of lattice varieties splits naturally into the study of modular lattice varieties and non-modular lattice varieties, dealt with in the second and third chapter respectively. Among the results discussed there are Freese's theorem that the variety of all modular lattices is not generated by its finite members, and several results concerning the question which varieties cover a given variety. The fourth chapter contains a proof of Baker's finite basis theorem and some results about the join of finitely based lattice varieties. Included in the last chapter is a characterisation of the amalgamation classes of certain congruence distributive varieties and the result that there are only three lattice varieties which have the amalgamation property. 2015-12-20T15:34:12Z 2015-12-20T15:34:12Z 1988 Master Thesis Masters MSc http://hdl.handle.net/11427/15851 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Lattice theory Jipsen, Peter Varieties of lattices |
| thesis_degree_str | Master's |
| title | Varieties of lattices |
| title_full | Varieties of lattices |
| title_fullStr | Varieties of lattices |
| title_full_unstemmed | Varieties of lattices |
| title_short | Varieties of lattices |
| title_sort | varieties of lattices |
| topic | Lattice theory |
| url | http://hdl.handle.net/11427/15851 |
| work_keys_str_mv | AT jipsenpeter varietiesoflattices |