Model Theory and Modules

by M. Prest

Overview

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.

Product Details

ISBN-13:	9780521348331
Publisher:	Cambridge University Press
Publication date:	02/25/1988
Series:	London Mathematical Society Lecture Note Series , #130
Pages:	400
Product dimensions:	5.98(w) x 8.98(h) x 0.91(d)

Table of Contents

Introduction; Acknowledgements; Notations and conventions; Remarks on the development of the area; Section summaries; 1. Some preliminaries; 2. Positive primitive formulas and the sets they define; 3. Stability and totally transcendental modules; 4. Hulls; 5. Forking and ranks; 6. Stability-theoretic properties of types; 7. Superstable modules; 8. The lattice of pp-types and free realisations of pp-types; 9. Types and the structure of pure-injective modules; 10. Dimension and decomposition; 11. Modules over artinian rings; 12. Functor categories; 13. Modules over artin algebras; 14. Projective and flat modules; 15. Torsion and torsionfree classes; 16. Elimination of quantifiers; 17. Decidability and undecidability; Problems page; Bibliography; Examples index; Notation index; Index.

Editorial 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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