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Purity, Spectra and Localisation

$210.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: July 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521873086

$210.00 (C)
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  • The central aim of this book is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localization is an ever-present theme and various types of spectrum play organizing roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.

    • Inclusion of relevant background material makes this suitable as an introduction for postgraduate students and researchers from other areas
    • Compiles a wide range of methods and results, some of which are previously unpublished, into one single, accessible source
    • Contains an extensive index, a detailed table of contents and thorough internal referencing
    Read more

    Reviews & endorsements

    "Prest's book is encyclopedic in scope. It will certainly serve as the bible of model theory of modules for years to come. However, it is also a book of examples: the interested reader can start with a very concrete example and watch how, as the book develops, this example treads on more and more abstract notions."
    Gena Puninski, Mathematical Reviews

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    Product details

    • Date Published: July 2009
    • format: Hardback
    • isbn: 9780521873086
    • length: 798 pages
    • dimensions: 240 x 164 x 45 mm
    • weight: 1.35kg
    • availability: In stock
  • Table of Contents

    Preface
    Introduction
    Part I. Modules:
    1. Pp conditions
    2. Purity
    3. Pp pairs and definable subcategories
    4. Pp-types and pure-injectivity
    5. The Ziegler spectrum
    6. Rings of definable scalars
    7. m-dimension and width
    8. Examples
    9. Ideals in mod-R
    A. Model theory
    Part II. Functors:
    10. Finitely presented functors
    11. Serre subcategories and localisation
    12. The Ziegler spectrum and injective functors
    13. Dimensions
    14. The Zariski spectrum and the sheaf of definable scalars
    15. Artin algebras
    16. Finitely accessible and presentable additive categories
    17. Spectra of triangulated categories
    B. Languages for definable categories
    C. A model theory/functor category dictionary
    Part III. Definable categories:
    18. Definable categories and interpretation functors
    D. Model theory of modules: an update
    E. Glossary
    Main examples
    Bibliography
    Index.

  • general resources

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email cflack@cambridge.org

  • Author

    Mike Prest, University of Manchester
    Mike Prest is Professor of Pure Mathematics at the University of Manchester.

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