LEADER 04616nam 2200589 450 001 9910480528503321 005 20170822131658.0 010 $a1-4704-0298-X 035 $a(CKB)3360000000464891 035 $a(EBL)3114442 035 $a(SSID)ssj0000976630 035 $a(PQKBManifestationID)11623605 035 $a(PQKBTitleCode)TC0000976630 035 $a(PQKBWorkID)11020690 035 $a(PQKB)10575876 035 $a(MiAaPQ)EBC3114442 035 $a(PPN)195415922 035 $a(EXLCZ)993360000000464891 100 $a20000908d2001 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe spectrum of a module category /$fHenning Krause 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2001. 215 $a1 online resource (143 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 707 300 $a"January 2001, Volume 149, Number 707 (second of 4 numbers)." 311 $a0-8218-2618-2 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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. a???-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"" 327 $a""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"" 327 $a""12.1. Reflective definable subcategories""""12.2. I??-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"" 327 $a""A.1. Localization in abelian categories""""A.2. Locally coherent Grothendieck categories""; ""A.3. Localization in locally coherent Grothendieck categories""; ""A.4. Locally noetherian categories""; ""Appendix B. Dimensions""; ""B.1. The dimension of an abelian category""; ""B.2. The dimension of a modular lattice""; ""Appendix C. Finitely presented functors and ideals""; ""C.1. The category of finitely presented functors""; ""C.2. Ideals in additive categories""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 707. 606 $aInjective modules (Algebra) 606 $aCategories (Mathematics) 608 $aElectronic books. 615 0$aInjective modules (Algebra) 615 0$aCategories (Mathematics) 676 $a510 s 676 $a512/.74 700 $aKrause$b Henning$f1962-$0932212 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480528503321 996 $aThe spectrum of a module category$92097244 997 $aUNINA