Model Theory and Modules

M. Prest (Author)

9780521348331, Cambridge University Press

Paperback, published 25 February 1988

400 pages
22.8 x 15.2 x 2.3 cm, 0.59 kg

"...contains a rich collection of concrete examples and exercises. It may be useful both as a reference book and as a texbook." Mathematical Reviews

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.

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.

Subject Areas: Mathematical logic [PBCD]