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Model Theory and Modules

Model Theory and Modules

$115.00 (C)

Part of London Mathematical Society Lecture Note Series

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

$ 115.00 (C)
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About the Authors
  • 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.

    Reviews & endorsements

    "...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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    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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