This up-to-date book provides a lucid and concise introduction to the theory of ordered sets and basic ordered algebraic structures. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field.

A unified introduction to the theory of ordered sets and basic ordered algebraic structures; it provides an exposition of all the essentials Up-to-date: it includes recent developments in the theory of residuated lattices and frames Includes numerous exercises and examples Includes supplementary material: sn.pub/extras

Klappentext

Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate.

The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Topics covered include:

[bulleted list]

residuated mappings

Galois connections

modular, distributive, and complemented lattices

Boolean algebras

pseudocomplemented lattices

Stone algebras

Heyting algebras

ordered groups

lattice-ordered groups representable groups

Archimedean ordered structures

ordered semigroups

naturally ordered regular and inverse Dubreil-Jacotin semigroups [end od bulleted list] Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field for researchers in mathematics, logic and computer science.

T. S. Blyth is Professor Emeritus at St. Andrews University, UK

Inhalt
Ordered sets; residuated mappings.- Lattices; lattice morphisms.- Regular equivalences.- Modular lattices.- Distributive lattices.- Complementation; boolean algebras.- Pseudocomplementation; Stone and Heyting algebras.- Congruences; subdirectly irreducible algebras.- Ordered groups.- Archimedean ordered structures.- Ordered semigroups; residuated semigroups.- Epimorphic group images; Dubreil-Jacotin semigroups.- Ordered regular semigroups.- Structure theorems.