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Representation theory of Artin algebras

Representation theory of Artin algebras (5회 대출)

자료유형
단행본
개인저자
Auslander, Maurice. Reiten, Idun, 1942- Smal? Sverre O.
서명 / 저자사항
Representation theory of Artin algebras / Maurice Auslander, Idun Reiten and Sverre O. Smal?
발행사항
Cambridge ;   New York, NY, USA :   Cambridge University Press,   1995.  
형태사항
xiv, 423 p. ; 24 cm.
총서사항
Cambridge studies in advanced mathematics ;36
ISBN
0521411343
서지주기
Includes bibliographical references (p. 413-419) and index.
일반주제명
Artin rings. Artin algebras. Representations of algebras. Anneaux artiniens. Repr?sentations d'alg?bre.
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.

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.4 A932r 등록번호 121021350 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차


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


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