It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim 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, localisation is an ever-present theme and various types of spectrum play organising 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- Compiles a wide range of methods and results, some of which are previously unpublished, into one single, accessible source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
'This book is an account of a fruitful interaction between algebra, mathematical logic, and category theory. … provides relevant background material and a wealth of illustrative examples. An extensive index and thorough referencing also make this book an ideal, comprehensive reference.' L'Enseignement MathématiqueSee more reviews
'This very interesting book is written so that it will be useful for graduate students and experienced researchers. It is worth to be mentioned that Mike Prest introduced in this book some very useful appendixes which come to help the reader to become familiar with the language of model theory. The book contains a lot of illuminating examples which are also very helpful for the reader.' Zentralblatt MATH
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: June 2009
- format: Hardback
- isbn: 9780521873086
- length: 798 pages
- dimensions: 240 x 164 x 45 mm
- weight: 1.35kg
- 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
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact firstname.lastname@example.org.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×