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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.Read more
- 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- Compiles a wide range of methods and results, some of which are previously unpublished, into one single, accessible source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
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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- Date Published: July 2009
- format: Hardback
- isbn: 9780521873086
- length: 798 pages
- dimensions: 240 x 164 x 45 mm
- weight: 1.32kg
- availability: In stock
Table of Contents
Part I. Modules:
1. Pp conditions
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
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
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
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