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Model Theory and Modules

Model Theory and Modules

£69.99

Part of London Mathematical Society Lecture Note Series

  • Author: M. Prest, University of Manchester
  • Date Published: February 1988
  • availability: Available
  • format: Paperback
  • isbn: 9780521348331

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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.

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    Product details

    • Date Published: February 1988
    • format: Paperback
    • isbn: 9780521348331
    • length: 400 pages
    • dimensions: 228 x 152 x 23 mm
    • weight: 0.59kg
    • availability: Available
  • 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.

  • Author

    M. Prest, University of Manchester

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