The spectrum of a module category / / Henning Krause

• Record Nr.: UNINA9910480528503321
• Autore: Krause Henning <1962->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2001
• ISBN: 1-4704-0298-X
• Descrizione fisica: 1 online resource (143 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 707
• Disciplina: 510 s; 512/.74
• Soggetti: Injective modules (Algebra); Categories (Mathematics); Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "January 2001, Volume 149, Number 707 (second of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Chapter 0. Introduction""; ""Chapter 1. The functor category""; ""1.1. Preliminaries""; ""1.2. Purity""; ""Chapter 2. Definable subcategories""; ""2.1. Definable subcategories""; ""2.2. Saturation""; ""2.3. The Ziegler topology""; ""2.4. Definable quotient categories""; ""2.5. Examples""; ""Chapter 3. Left approximations""; ""3.1. Left almost split maps""; ""3.2. Left approximations""; ""3.3. Minimal left approximations""; ""Chapter 4. Duality""; ""4.1. Purely equivalent and purely opposed modules""; ""4.2. The dual of a definable subcategory""; ""4.3. Pure-reflexive modules""; ""Chapter 5. Ideals in the category of finitely presented modules""""5.1. Fp-idempotent ideals""; ""5.2. Ideals generated by idempotents""; ""Chapter 6. Endofinite modules""; ""6.1. The endocategory of a module""; ""6.2. â??-pure-injective modules""; ""6.3. Product-complete modules""; ""6.4. Endofinite modules""; ""6.5. Generic modules""; ""6.6. Ideals of finite length""; ""Chapter 7. Krull-Gabriel dimension""; ""7.1. The Krull-Gabriel dimension of a ring""; ""7.2. The Krull-Gabriel dimension of a module""; ""Chapter 8. The infinite radical""; ""8.1. The preinjective dimension of a module""; ""8.2. Transfinite powers of the Jacobson radical""""Chapter 9. Functors between module categories""; ""9.1. Coherent functors""; ""Chapter 10. Tame algebras""; ""10.1. Endofinitely tame algebras""; ""10.2. Functors ; preserving tameness""; ""10.3. Representation embeddings""; ""10.4. One-parameter families and generic modules""; ""Chapter 11. Rings of definable scalars""; ""11.1. Rings of definable scalars""; ""11.2. Calculus of fractions""; ""11.3. Biendomorphism rings""; ""11.4. Basic properties""; ""11.5. Epimorphisms of rings""; ""Chapter 12. Reflective definable subcategories""; ""12.1. Reflective definable subcategories""""12.2. Î?-continuous modules""; ""12.3. Definable and universal localizations""; ""Chapter 13. Sheaves""; ""13.1. Sheaves on the Gabriel spectrum""; ""13.2. The Zariski topology""; ""13.3. Structure sheaves""; ""13.4. Associated sheaves of modules""; ""Chapter 14. Tame hereditary algebras""; ""14.1. Preliminaries""; ""14.2. A parametrizing curve""; ""Chapter 15. Coherent rings""; ""15.1. Preliminaries""; ""15.2. Prime spectrum versus Gabriel spectrum""; ""15.3. The global section functor""; ""Appendix A. Locally coherent Grothendieck categories""; ""A.1. Localization in abelian categories""""A.2. Locally coherent Grothendieck categories""; ""A.3. Localization in locally coherent Grothendieck categories""; ""A.4. Locally noetherian categories""; ""Appendix B. Dimensions""; ""B.1. The dimension of an abelian category""; ""B.2. The dimension of a modular lattice""; ""Appendix C. Finitely presented functors and ideals""; ""C.1. The category of finitely presented functors""; ""C.2. Ideals in additive categories""; ""Bibliography""