04616nam 2200589 450 991048052850332120170822131658.01-4704-0298-X(CKB)3360000000464891(EBL)3114442(SSID)ssj0000976630(PQKBManifestationID)11623605(PQKBTitleCode)TC0000976630(PQKBWorkID)11020690(PQKB)10575876(MiAaPQ)EBC3114442(PPN)195415922(EXLCZ)99336000000046489120000908d2001 uy| 0engur|n|---|||||txtccrThe spectrum of a module category /Henning KrauseProvidence, Rhode Island :American Mathematical Society,2001.1 online resource (143 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 707"January 2001, Volume 149, Number 707 (second of 4 numbers)."0-8218-2618-2 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;no. 707.Injective modules (Algebra)Categories (Mathematics)Electronic books.Injective modules (Algebra)Categories (Mathematics)510 s512/.74Krause Henning1962-932212MiAaPQMiAaPQMiAaPQBOOK9910480528503321The spectrum of a module category2097244UNINA