# Lattices and Ordered Algebraic Structures

• T.S. Blyth
Textbook

Part of the Universitext book series (UTX)

1. Front Matter
Pages I-IX
2. Pages 1-18
3. Pages 19-38
4. Pages 39-48
5. Pages 49-64
6. Pages 65-76
7. Pages 77-102
8. Pages 103-118
9. Pages 119-142
10. Pages 143-170
11. Pages 171-192
12. Pages 193-206
13. Pages 207-224
14. Pages 225-264
15. Pages 265-292
16. Back Matter
Pages 293-303

### Introduction

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

### Keywords

Algebraic structure Algebraic structures Boolean algebra Lattice Lattices Ordered groups Ordered semigroups Ordered sets algebra logic sets

#### Authors and affiliations

• T.S. Blyth
• 1
1. 1.School of Mathematics and Statistics, Mathematical InstituteUniversity of St AndrewsSt AndrewsUK