分配格序代數

內容介紹

《分配格序代數(英文版）》內容簡介：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.

作品目錄

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