Purity, spectra and localisation
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 boo...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2009
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| Series: | Encyclopedia of mathematics and its applications
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Pp conditions
- Purity
- Pp-pairs and definable subcategories
- Pp-types and pure-injectivity
- The Ziegler spectrum
- Rings of definable scalars
- M-dimension and width
- Examples
- Ideals in mod-R
- Finitely presented functors
- Serre subcategories and localisation
- The Ziegler spectrum and injective functors
- Dimensions
- The Zariski spectrum and the sheaf of definable scalars
- Artin algebras
- Finitely accessible and presentable additive categories
- Spectra of triangulated categories
- Definable categories and interpretation functors