Lattices and Ordered Algebraic Structures

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