Lattice Theory, Volume 25, Part 2

Front Cover
American Mathematical Soc., Dec 31, 1940 - Mathematics - 418 pages
Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. It is excellent reading, and ... the best place to start when one wishes to explore some portion of lattice theory or to appreciate the general flavor of the field. --Bulletin of the AMS
 

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Contents

CHAPTER
ix
POSTULATES FOR LATTICES
20
STRUCTURE AND REPRESENTATION THEORY
55
GEOMETRIC LATTICES
80
COMPLETE LATTICES
111
UNIVERSAL ALGEBRA
132
APPLICATIONS TO ALGEBRA
159
TRANSFINITE INDUCTION
180
CHAPTER XII
277
LATTICEORDERED GROUPS
287
LATTICEORDERED MONOIDS
319
CHAPTER XV
347
POSITIVE LINEAR OPERATORS
380
LATTICEORDERED RINGS
397
BIBLIOGRAPHY
411
INDEX
417

APPLICATIONS TO GENERAL TOPOLOGY
211
BOREL ALGEBRAS AND VON NEUMANN LATTICES
254

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