Model Theory and Modules

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Paperback | 25 April 1988

At a Glance

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400 Pages

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22.86 x 15.24 x 2.26

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In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a 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. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.

Industry Reviews

"...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

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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.

Model Theory and Modules

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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