Memoirs of the American Mathematical Society
2001;
125 pp;
Softcover
MSC: Primary 16;
Secondary 18
Print ISBN: 978-0-8218-2618-8
Product Code: MEMO/149/707
List Price: $57.00
AMS Member Price: $34.20
MAA Member Price: $51.30
Electronic ISBN: 978-1-4704-0298-3
Product Code: MEMO/149/707.E
List Price: $57.00
AMS Member Price: $34.20
MAA Member Price: $51.30
The Spectrum of a Module Category
Share this pageHenning Krause
These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.
Readership
Graduate students and research mathematicians interested in associative rings and algebras.
Table of Contents
Table of Contents
The Spectrum of a Module Category
- Contents vii8 free
- Chapter 0. Introduction 112 free
- Chapter 1. The functor category 1122 free
- Chapter 2. Definable subcategories 1526
- Chapter 3. Left approximations 2435
- Chapter 4. Duality 3142
- Chapter 5. Ideals in the category of finitely presented modules 3748
- Chapter 6. Endofinite modules 4354
- Chapter 7. Krull-Gabriel dimension 5465
- Chapter 8. The infinite radical 5869
- Chapter 9. Functors between module categories 6475
- Chapter 10. Tame algebras 6879
- Chapter 11. Rings of definable scalars 7384
- Chapter 12. Reflective definable subcategories 8293
- Chapter 13. Sheaves 89100
- Chapter 14. Tame hereditary algebras 98109
- Chapter 15. Coherent rings 105116
- Appendix A. Locally coherent Grothendieck categories 111122
- Appendix B. Dimensions 116127
- Appendix C. Finitely presented functors and ideals 119130
- Bibliography 122133