| 000 | 01043camuuu200313 a 4500 | |
| 001 | 000000450716 | |
| 003 | OCoLC | |
| 005 | 19961122154809.0 | |
| 008 | 931105s1995 enk b 001 0 eng | |
| 010 | ▼a 93043326 //r95 | |
| 020 | ▼a 0521411343 | |
| 040 | ▼a DLC ▼c DLC ▼d GZM ▼d FPU | |
| 049 | ▼a ACSL ▼l 121021350 | |
| 050 | 0 0 | ▼a QA251.5 ▼b .A87 1994 |
| 082 | 0 0 | ▼a 512/.4 ▼2 20 |
| 090 | ▼a 512.4 ▼b A932r | |
| 100 | 1 | ▼a Auslander, Maurice. |
| 245 | 1 0 | ▼a Representation theory of Artin algebras / ▼c Maurice Auslander, Idun Reiten and Sverre O. Smal？ |
| 260 | ▼a Cambridge ; ▼a New York, NY, USA : ▼b Cambridge University Press, ▼c 1995. | |
| 300 | ▼a xiv, 423 p. ; ▼c 24 cm. | |
| 440 | 0 | ▼a Cambridge studies in advanced mathematics ; ▼v 36 |
| 504 | ▼a Includes bibliographical references (p. 413-419) and index. | |
| 650 | 0 | ▼a Artin rings. |
| 650 | 0 | ▼a Artin algebras. |
| 650 | 0 | ▼a Representations of algebras. |
| 650 | 7 | ▼a Anneaux artiniens. ▼2 ram |
| 650 | 7 | ▼a Repr？sentations d'alg？bre. ▼2 ram |
| 700 | 1 | ▼a Reiten, Idun, ▼d 1942- |
| 700 | 1 | ▼a Smal？ Sverre O. |
Holdings Information
| No. | Location | Call Number | Accession No. | Availability | Due Date | Make a Reservation | Service |
|---|---|---|---|---|---|---|---|
| No. 1 | Location Science & Engineering Library/Sci-Info(Stacks2)/ | Call Number 512.4 A932r | Accession No. 121021350 | Availability Available | Due Date | Make a Reservation | Service |
Contents information
Table of Contents
CONTENTS Introduction = xi Ⅰ Artin rings = 1 1 Finite length modules = 1 2 Right and left minimal morphisms = 6 3 Radical of rings and modules = 8 4 Structure of projective modules = 12 5 Some homological facts = 16 Exercises = 23 Notes = 25 Ⅱ Artin algebras = 26 1 Artin algebras and categories = 26 2 Projectivization = 32 3 Duality = 37 4 Structure of injective modules = 39 5 Blocks = 43 Exercises = 45 Notes = 47 Ⅲ Examples of algebras and modules = 49 1 Quivers and their representations = 49 2 Triangular matrix rings = 70 3 Group algebras = 79 4 Skew group algebras = 83 Excercises = 94 Notes = 99 Ⅳ The transpose and the dual = 100 1 The transpose = 100 2 Nakayama algebras = 111 3 Selfinjective algebras = 122 4 Defect of exact sequences = 128 Exercises = 133 Notes = 135 Ⅴ Almost split sequences = 136 1 Almost split sequences and morphisms = 136 2 Interpretation and examples = 147 3 Projective or injective middle terms = 153 4 Group algebras = 158 5 Irreducible morphisms = 166 6 The middle term = 173 7 The radical = 178 Exercises = 185 Notes = 189 Ⅵ Finite representation type = 191 1 A criterion = 191 2 Nakayama algebras = 197 3 Group algebras = 200 4 Grothendieck groups = 206 5 Auslander algebras = 209 Exercises = 219 Notes = 221 Ⅶ The Auslander-Reiten-quiver = 224 1 The Auslander-Reiten-quiver = 224 2 Auslander-Reiten-quivers and finite type = 232 3 Cartan matrices = 241 4 Translation quivers = 248 Exercises = 253 Notes = 256 Ⅷ Hereditary algebras = 257 1 Preprojective and preinjective modules = 258 2 The Coxeter transformaton = 269 3 The homological quadratic form = 272 4 Regular components = 277 5 Finite representation type = 288 6 Quadratic forms and roots = 294 7 Kronecker algebras = 302 Exercises = 309 Notes = 311 Ⅸ Short chains and cycles = 313 1 Short cycles = 313 2 Modules determined by composition factors = 320 3 Sincere modules and short cycles = 323 4 Modules determined by their top and socle = 326 Exercises = 332 Notes = 333 Ⅹ Stable equivalence = 335 1 Stable equivalence and almost split sequences = 335 2 Artin algebras with radical square zero = 344 3 Symmetric Nakayama algebras = 352 Exercises = 362 Notes = 364 XI Modules determining morphisms = 365 1 Morphisms determined by a module = 365 2 Modules determining a morphism = 370 3 Classification of morphisms = 379 4 Rigid exact sequences = 385 5 Indecomposable middle terms = 389 Exercises = 399 Notes = 405 Notation = 406 Conjectures = 409 Open problems = 411 Bibliography = 413 Relevant conference proceedings = 420 Index = 421