分配格序代數(shù)

內(nèi)容概要

　　With the development of information science
and theoretical computer science, lattice-ordered algebraic
structure theory has played a more and more important role in
theoretical and applied science. Not only is it an important branch
of modern mathematics, but it also has broad and important
applications in algebra, topology, fuzzy mathematics and other
applied sciences such as coding theory, computer programs,
multi-valued logic and science of information systems, etc. The
research in distributive lattices with unary operations has made
great progress in the past three decades, since Joel Berman first
introduced the distributive lattices with an additional unary
operation in 1978, which were named Ockham algebras by Goldberg a
year later. This is due to those researchers who are working on
this subject, such as Adams, Beazer, Berman, Blyth, Davey,
Goldberg, Priestley, Sankappanavar and Varlet.
　　

書(shū)籍目錄

foreword
preface
chapter 1 universal algebra and lattice-ordered algebras
1.1 universal algebra
1.2 lattice-ordered algebras
1.3 priestley duality of lattice-ordered algebras
chapter 2 ockham algebras
2.1 subclasses
2.2 the subdirectly irreducible algebras
2.3 ockham chains
2.4 the structures of finite simple ockham algebras
2.5 isotone mappings on ockham algebras
chapter 3 extended ockham algebras
3.1 definition and basic congruences
3.2 the subdirectly irreducible algebras
3.3 symmetric extended de morgan algebras
chapter 4 double ockham algebras
4.1 notions and basic results
4.2 commuting double ockham algebras
4.3 balanced double ockham algebras
chapter 5 pseudocomplemented and demi-pseudocomplemerited
algebras
5.1 pseudocomplemented algebras
5.2 the subdirectly irreducible p-algebras
5.3 double pseudocomplemented algebras
5.4 ideals and filters
5.5 demi-pseudocomplemented algebras
chapter 6 ockham algebras with pseudocomplementation 6.1 notions
and basic results
6.2 the structure of congruence lattices
6.3 the subdirectly irreducible algebras
6.4 the subvarieties of variety pk1,1
6.5 ideals and filters in po-algebras
chapter 7 oekham algebras with double pseudocomplementation
7.1 notions and properties
7.2 the structure of the subdirectly irreducible algebras
chapter 8 ockham algebras with balanced pseudocomplementation
8.1 introduction
8.2 the structures of the congruence lattices
8.3 priestley duality and subdirectly irreducible algebras
8.4 equational bases
8.5 the subvarieties of bpo determined by axioms
chapter 9 ockham algebras with demi-pseudocomplementation
9.1 notions and basic results
9.2 k1,1-algebras with demi-pseudocomplementation
9.3 weak stone-ockham algebras
chapter 10 ockham algebras with balanced
demipseudocomplementation
10.1 basic results
10.2 the subdirectly irreducible algebras
chapter 11 coherent congruences on some lattice-ordered
algebras
ll.1 introduction
11.2 on double ms-algebras
11.3 on symmetric extended de morgan algebras
chapter 12 the endomorphism kernel property in ockham
algebras
12.1 the endomorphism kernel property
12.2 ockham algebras
12.3 de morgan algebras
bibliography
notation index
index

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