Congruences on lattices (with application to amalgamation)

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 fini...

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Main Author: Laing, Lyneve
Other Authors: Rose, Henry
Format: Dissertation
Language:English
Published: University of Cape Town 2016
Subjects:
Online Access:http://hdl.handle.net/11427/17442
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spelling ndltd-netd.ac.za-oai-union.ndltd.org-uct-oai-localhost-11427-174422020-10-06T05:10:53Z 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 University of Cape Town Faculty of Science Department of Mathematics and Applied Mathematics
collection NDLTD
language English
format Dissertation
sources NDLTD
topic Mathematics
spellingShingle Mathematics
Laing, Lyneve
Congruences on lattices (with application to amalgamation)
description 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.
author2 Rose, Henry
author_facet Rose, Henry
Laing, Lyneve
author Laing, Lyneve
author_sort Laing, Lyneve
title Congruences on lattices (with application to amalgamation)
title_short 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_sort congruences on lattices (with application to amalgamation)
publisher University of Cape Town
publishDate 2016
url http://hdl.handle.net/11427/17442
work_keys_str_mv AT lainglyneve congruencesonlatticeswithapplicationtoamalgamation
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