Rings and their modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2011
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 452 S. graph. Darst. |
| ISBN: | 9783110250220 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804143797301411840 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE V
ABOUT THE TEXT V
ACKNOWLEDGEMENTS VIII
0 PRELIMINARIES 1
0.1 CLASSES, SETS AND FUNCTIONS 1
PARTIAL ORDERS AND EQUIVALENCE RELATIONS 2
ZORN S LEMMA AND WELL-ORDERING 3
0.2 ORDINAL AND CARDINAL NUMBERS 4
0.3 COMMUTATIVE DIAGRAMS 4
0.4 NOTATION AND TERMINOLOGY 4
PROBLEM SET 5
1 BASIC PROPERTIES OF RINGS AND MODULES 7
1.1 RINGS 7
PROBLEM SET 1.1 12
1.2 LEFT AND RIGHT IDEALS 14
FACTOR RINGS 17
PROBLEM SET 1.2 17
1.3 RING HOMOMORPHISMS 21
PROBLEM SET 1.3 24
1.4 MODULES 25
FACTOR MODULES 29
PROBLEM SET 1.4 30
1.5 MODULE HOMOMORPHISMS 32
PROBLEM SET 1 .5 36
2 FUNDAMENTAL CONSTRUCTIONS 39
2.1 DIRECT PRODUCTS AND DIRECT SUMS 39
DIRECT PRODUCTS 39
EXTERNAL DIRECT SUMS 43
INTERNAL DIRECT SUMS 45
PROBLEM SET 2.1 49
2.2 FREE MODULES 51
RINGS WITH INVARIANT BASIS NUMBER 56
PROBLEM SET 2.2 60
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009312561
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.3 TENSOR PRODUCTS OF MODULES 63
PROBLEM SET 2.3 69
CATEGORIES 71
3.1 CATEGORIES 71
FUNCTORS 75
PROPERTIES OF MORPHISMS 77
PROBLEM SET 3.1 79
3.2 EXACT SEQUENCES IN MOD 82
SPLIT SHORT EXACT SEQUENCES 84
PROBLEM SET 3.2 86
3.3 HORN AND AS FUNCTORS 90
PROPERTIES OF HORN 90
PROPERTIES OF TENSOR PRODUCTS 94
PROBLEM SET 3.3 95
3.4 EQUIVALENT CATEGORIES AND ADJOINT FUNCTORS 97
ADJOINTS 99
PROBLEM SET 3.4 102
CHAIN CONDITIONS 104
4.1 GENERATING AND COGENERATING CLASSES 104
PROBLEM SET 4.1 106
4.2 NOETHERIAN AND ARTINIAN MODULES 107
PROBLEM SET 4.2 118
4.3 MODULES OVER PRINCIPAL IDEAL DOMAINS 120
FREE MODULES OVER A PID 124
FINITELY GENERATED MODULES OVER A PID 128
PROBLEM SET 4.3 134
INJECTIVE, PROJECTIVE, AND FLAT MODULES 135
5.1 INJECTIVE MODULES 135
INJECTIVE MODULES AND THE FUNCTOR HORN/? (-, M) 140
PROBLEM SET 5.1 142
5.2 PROJECTIVE MODULES 144
PROJECTIVE MODULES AND THE FUNCTOR HORN (A/,-) 148
HEREDITARY RINGS 148
SEMIHEREDITARY RINGS 151
PROBLEM SET 5.2 152
5.3 FLAT MODULES 154
FLAT MODULES AND THE FUNCTOR M S R - 154
COHERENT RINGS 159
REGULAR RINGS AND FLAT MODULES 163
IMAGE 3
CONTENTS XI
PROBLEM SET 5.3 165
5.4 QUASI-INJECTIVE AND QUASI-PROJECTIVE MODULES 169
PROBLEM SET 5.4 170
6 CLASSICAL RING THEORY 171
6.1 THE JACOBSON RADICAL 171
PROBLEM SET 6.1 177
6.2 THE PRIME RADICAL 178
PRIME RINGS 179
SEMIPRIME RINGS 184
PROBLEM SET 6.2 186
6.3 RADICALS AND CHAIN CONDITIONS 188
PROBLEM SET 6.3 190
6.4 WEDDERBURN-ARTIN THEORY 191
PROBLEM SET 6.4 203
6.5 PRIMITIVE RINGS AND DENSITY 205
PROBLEM SET 6.5 210
6.6 RINGS THAT ARE SEMISIMPLE 211
PROBLEM SET 6.6 215
7 ENVELOPES AND COVERS 216
7.1 INJECTIVE ENVELOPES 216
PROBLEM SET 7.1 219
7.2 PROJECTIVE COVERS 221
THE RADICAL OF A PROJECTIVE MODULE 223
SEMIPERFECT RINGS 227
PERFECT RINGS 237
PROBLEM SET 7.2 241
7.3 QI-ENVELOPES AND QP-COVERS 245
QUASI-INJECTIVE ENVELOPES 245
QUASI-PROJECTIVE COVERS 248
PROBLEM SET 7.3 252
8 RINGS AND MODULES OF QUOTIENTS 254
8.1 RINGS OF QUOTIENTS 254
THE NONCOMMUTATIVE CASE 254
THE COMMUTATIVE CASE 261
PROBLEM SET 8.1 262
8.2 MODULES OF QUOTIENTS 264
PROBLEM SET 8.2 267
8.3 GOLDIE S THEOREM 270
PROBLEM SET 8.3 276
IMAGE 4
XII CONTENTS
8.4 THE MAXIMAL RING OF QUOTIENTS 277
PROBLEM SET 8.4 291
9 GRADED RINGS AND MODULES 294
9.1 GRADED RINGS AND MODULES 294
GRADED RINGS 294
GRADED MODULES 299
PROBLEM SET 9.1 305
9.2 FUNDAMENTAL CONCEPTS 308
GRADED DIRECT PRODUCTS AND SUMS 309
GRADED TENSOR PRODUCTS 311
GRADED FREE MODULES 312
PROBLEM SET 9.2 313
9.3 GRADED PROJECTIVE, GRADED INJECTIVE AND GRADED FLAT MODULES . . ..
314 GRADED PROJECTIVE AND GRADED INJECTIVE MODULES 314
GRADED FLAT MODULES 318
PROBLEM SET 9.3 319
9.4 GRADED MODULES WITH CHAIN CONDITIONS 320
GRADED NOETHERIAN AND GRADED ARTINIAN MODULES 320
PROBLEM SET 9.4 325
9.5 MORE ON GRADED RINGS 325
THE GRADED JACOBSON RADICAL 325
GRADED WEDDERBURN-ARTIN THEORY 327
PROBLEM SET 9.5 329
10 MORE ON RINGS AND MODULES 331
10.1 REFLEXIVITY AND VECTOR SPACES 332
PROBLEM SET 10.1 334
10.2 REFLEXIVITY AND ^-MODULES 335
SELF-INJECTIVE RINGS 336
KASCH RINGS AND INJECTIVE COGENERATORS 339
SEMIPRIMARY RINGS 341
QUASI-FROBENIUS RINGS 342
PROBLEM SET 10.2 346
11 INTRODUCTION TO HOMOLOGICAL ALGEBRA 348
11.1 CHAIN AND COCHAIN COMPLEXES 348
HOMOLOGY AND COHOMOLOGY SEQUENCES 353
PROBLEM SET 11.1 357
11.2 PROJECTIVE AND INJECTIVE RESOLUTIONS 359
PROBLEM SET 11.2 365
11.3 DERIVED FUNCTORS 367
IMAGE 5
CONTENTS XIII
PROBLEM SET 11.3 372
11.4 EXTENSION FUNCTORS 373
RIGHT DERIVED FUNCTORS OF HORN R(-,X) 373
RIGHT DERIVED FUNCTORS OF HORN/; (X,-) 381
PROBLEM SET 11.4 386
11.5 TORSION FUNCTORS 390
LEFT DERIVED FUNCTORS OF - R X AND X R - 390
PROBLEM SET 11.5 394
12 HOMOLOGICAL METHODS 395
12.1 PROJECTIVE AND INJECTIVE DIMENSION 395
PROBLEM SET 12.1 402
12.2 FLAT DIMENSION 403
PROBLEM SET 12.2 407
12.3 DIMENSION OF POLYNOMIAL RINGS 409
PROBLEM SET 12.3 417
12.4 DIMENSION OF MATRIX RINGS 417
PROBLEM SET 12.4 421
12.5 QUASI-FROBENIUS RINGS REVISITED 421
MORE ON REFLEXIVE MODULES 421
PROBLEM SET 12.5 428
A ORDINAL AND CARDINAL NUMBERS 429
ORDINAL NUMBERS 429
CARDINAL NUMBERS 433
PROBLEM SET 435
BIBLIOGRAPHY 437
LIST OF SYMBOLS 441
INDEX 443
|
| any_adam_object | 1 |
| author | Bland, Paul E. |
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| dewey-full | 512.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.4 |
| dewey-search | 512.4 |
| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037206263 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:22Z |
| institution | BVB |
| isbn | 9783110250220 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021120413 |
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| owner_facet | DE-19 DE-BY-UBM DE-11 DE-703 DE-634 DE-20 DE-824 |
| physical | XIII, 452 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | de Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Bland, Paul E. Verfasser (DE-588)118175424 aut Rings and their modules Paul E. Bland Berlin [u.a.] de Gruyter 2011 XIII, 452 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Modultheorie (DE-588)4170336-4 gnd rswk-swf Ringtheorie (DE-588)4126571-3 s Modultheorie (DE-588)4170336-4 s Homologische Algebra (DE-588)4160598-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-025023-7 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021120413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bland, Paul E. Rings and their modules Homologische Algebra (DE-588)4160598-6 gnd Ringtheorie (DE-588)4126571-3 gnd Modultheorie (DE-588)4170336-4 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4126571-3 (DE-588)4170336-4 |
| title | Rings and their modules |
| title_auth | Rings and their modules |
| title_exact_search | Rings and their modules |
| title_full | Rings and their modules Paul E. Bland |
| title_fullStr | Rings and their modules Paul E. Bland |
| title_full_unstemmed | Rings and their modules Paul E. Bland |
| title_short | Rings and their modules |
| title_sort | rings and their modules |
| topic | Homologische Algebra (DE-588)4160598-6 gnd Ringtheorie (DE-588)4126571-3 gnd Modultheorie (DE-588)4170336-4 gnd |
| topic_facet | Homologische Algebra Ringtheorie Modultheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021120413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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