Model Theory and Modules

Häftad, Engelska, 1988

Del 130 i serien London Mathematical Society Lecture Note Series

1 240 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1988-02-25
Mått:152 x 228 x 23 mm
Vikt:590 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Lecture Note Series
Antal sidor:400
Förlag:Cambridge University Press
ISBN:9780521348331

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Recensioner i media

"...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

Innehållsförteckning

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.