Lattices and Ordered Algebraic Structures

✍ Scribed by T.S. Blyth

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 311
• Series: Universitext
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning.…The exposition is thorough and all proofs that the reviewer checked were highly polished.…Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS

✦ Table of Contents

Cover......Page 1
Lattices and Ordered
Algebraic Structures......Page 3
Universitext......Page 2
ISBN 1852339055......Page 4
Preface......Page 5
Contents......Page 7
1
Ordered sets; residuated mappings......Page 10
2
Lattices; lattice morphisms......Page 28
3
Regular equivalences......Page 48
4
Modular lattices......Page 58
5
Distributive lattices......Page 74
6
Complementation; boolean algebras......Page 86
7
Pseudocomplementation; Stone and Heyting
algebras......Page 112
8
Congruences; subdirectly irreducible algebras......Page 128
9
Ordered groups......Page 152
10
Archimedean ordered structures......Page 180
11
Ordered semigroups; residuated semigroups......Page 202
12
Epimorphic group images; Dubreil-Jacotin
semigroups......Page 216
13
Ordered regular semigroups......Page 234
14
Structure theorems......Page 274
References......Page 302