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...
Main Author: | |
---|---|
Other Authors: | |
Format: | Dissertation |
Language: | English |
Published: |
University of Cape Town
2016
|
Subjects: | |
Online Access: | http://hdl.handle.net/11427/17442 |
id |
ndltd-netd.ac.za-oai-union.ndltd.org-uct-oai-localhost-11427-17442 |
---|---|
record_format |
oai_dc |
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 |
_version_ |
1719347726910488576 |