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Model Theory and Modules : London Mathematical Society Lecture Note Series - Mike Prest

Model Theory and Modules

London Mathematical Society Lecture Note Series

By: Mike Prest, N. J. Hitchin (Editor)

Paperback

Published: 25th April 1988
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Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules.

"...absolutely essential to anyone with any interest in the subject matter, because of its comprehensiveness, currency, well-written style, and extensive bibliographical references." Journal of Symbolic Logic "...contains a rich collection of concrete examples and exercises. It may be useful both as a reference book and as a texbook." Mathematical Reviews

Introduction
Acknowledgements
Notations and conventions
Remarks on the development of the area
Section summaries
Some preliminaries
Positive primitive formulas and the sets they define
Stability and totally transcendental modules
Hulls
Forking and ranks
Stability-theoretic properties of types
Superstable modules
The lattice of pp-types and free realisations of pp-types
Types and the structure of pure-injective modules
Dimension and decomposition
Modules over artinian rings
Functor categories
Modules over artin algebras
Projective and flat modules
Torsion and torsionfree classes
Elimination of quantifiers
Decidability and undecidability
Problems page
Bibliography
Examples index
Notation index
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521348331
ISBN-10: 0521348331
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 400
Published: 25th April 1988
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.3
Weight (kg): 0.59