Modules over non-noetherian domains:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2001]
|
| Series: | Mathematical surveys and monographs
Volume 84 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 613 Seiten |
| ISBN: | 0821819631 9780821819630 |
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MARC
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| 245 | 1 | 0 | |a Modules over non-noetherian domains |c László Fuchs ; Luigi Salce |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2001] | |
| 264 | 4 | |c © 2001 | |
| 300 | |a xiii, 613 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 84 | |
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Record in the Search Index
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| adam_text | Table of Contents
Preface xi
List of Symbols xv
Chapter I. Commutative Domains and Their Modules
1. Generalities on domains 1
2. Fractional ideals 9
3. Integral dependence 16
4. Module categories 22
5. Lemmas on Horn and Ext 27
6. Lemmas on tensor and torsion products 32
7. Divisibility and relative divisibility 36
8. Pure submodules 42
9. The exchange property 49
10. Semilocal endomorphism rings 52
Notes 55
Chapter II. Valuation Domains
1. Fundamental properties of valuation domains 57
2. Totally ordered abelian groups 60
3. Valuations 64
4. Ideals of valuation domains 68
5. The class semigroup 73
6. Maximal and almost maximal valuation domains 77
7. Henselian valuation rings 80
8. Strongly discrete valuation domains 86
Notes 89
Chapter III. Priifer Domains
1. Fundamental properties and characterizations 91
2. Priifer domains of finite character 97
3. The class semigroup 100
4. Lattice ordered abelian groups 107
5. Bezout domains 112
6. Elementary divisor domains 115
7. Strongly discrete Priifer domains 119
Notes 121
vii
viii TABLE OF CONTENTS
Chapter IV. More Non Noetherian Domains
1. Krull domains 123
2. Coherent domains 128
3. /i Local domains 131
4. Matlis domains 137
5. Reflexive domains 142
Notes 147
Chapter V. Finitely Generated Modules
1. Cyclic modules 149
2. Finitely generated modules 152
3. Finitely presented modules 157
4. Finite presentations 161
5. Finitely generated modules over valuation domains 167
6. Indecomposable finitely generated modules 171
7. Finitely generated modules with local endomorphism rings 177
8. Decompositions of finitely generated modules 180
9. Finitely generated modules without the Krull Schmidt property ... 185
10. Domains whose finitely generated modules are direct sums of cyclics 189
Notes 191
Chapter VI. Projectivity and Projective Dimension
1. Projective modules 195
2. Projective dimension 201
3. Projective dimension over valuation domains 206
4. Global projective dimension of Priifer domains 212
5. Tight submodules 214
6. Modules of projective dimension one 216
7. Equivalent presentations 219
8. Stacked bases over /i local Priifer domains 224
9. Flat modules 229
10. Weak dimension 235
11. Quasi projective modules 237
12. Pure and flD projectivity 240
Notes 245
Chapter VII. Divisible Modules
1. Divisible modules 247
2. /i Divisible modules, Matlis domains 251
3. Divisible modules over valuation domains 255
4. Categories of divisible modules 260
5. Indecomposable divisible modules 265
6. Superdecomposable divisible modules 269
Notes 272
Chapter VIII. Topology and Filtration
1. The fl topology 273
2. Complete torsion free modules. The Matlis category equivalence .. 278
TABLE OF CONTENTS ix
3. Completions of ideals 282
4. ^ Completions over Matlis domains 285
5. Cokernels of fi completions 290
6. Weakly cotorsion modules 292
7. Linear compactness 296
8. Filtration and ultracompleteness 300
Notes 302
Chapter IX. Injective Modules
1. Injectivity 305
2. Indecomposable injectives 309
3. Absolute purity 312
4. Injectives over valuation and Priifer domains 315
5. E Injectives 319
6. Injectives over Krull domains 324
7. Injective dimension 331
8. Quasi injective modules 333
Notes 335
Chapter X. Uniserial Modules
1. Generalities on uniserial modules 337
2. Endomorphism rings of uniserial modules 341
3. Uniserial modules over valuation domains 344
4. Existence of non standard uniserial modules 348
5. More on the existence of non standard uniserial modules 352
6. Kaplansky s problem 356
7. The threshold submodules 359
8. Life span of uniserial modules 364
9. Uniserial modules of the same level 367
10. The monoid Unis R 373
Notes 379
Chapter XI. Heights, Invariants and Basic Submodules
1. Heights 381
2. Equiheight, nice and balanced submodules 384
3. Indicators 387
4. Invariants 389
5. Basic submodules 392
6. Modules with trivial invariants 396
Notes 402
Chapter XII. Polyserial Modules
1. Polyserial and weakly polyserial modules 403
2. Direct sums of uniserial modules 407
3. Monoserial modules 410
4. Episerial modules and their submodules 414
5. Direct decompositions of weakly polyserial modules 419
Notes 421
X TABLE OF CONTENTS
Chapter XIII. RD and Pure Injectivity
1. RZMnjective modules 423
2. Pure injective modules 430
3. Algebraic compactness 434
4. Pure injective modules over Priifer domains 441
5. Pure injective modules over valuation domains 444
6. Pure injectivity over coherent domains 451
7. Nj Compact modules 452
8. Cotorsion modules 457
Notes 461
Chapter XIV. Torsion Modules
1. Decompositions of torsion modules 463
2. Torsion modules of projective dimension one 465
3. Simple presentation 468
4. Balanced submodules 475
5. Simply presented torsion modules 479
6. Torsion complete modules 483
Notes 487
Chapter XV. Torsion Free Modules of Finite Rank
1. Preliminaries 489
2. Direct sums of ideals 493
3. Torsion free modules over valuation domains 496
4. £ Domains 500
5. Indecomposable modules 504
6. Indecomposability over valuation domains 509
7. Direct decompositions of torsion free modules 513
8. Warfield domains 520
9. Intrinsic characterization of Warfield domains 526
Notes 529
Chapter XVI. Infinite Rank Torsion Free Modules
1. Chains of projective modules 531
2. Almost projective modules 537
3. Balancedness 541
4. Balanced projective dimension 547
5. Separable modules 551
6. Slender modules 553
7. Large indecomposable modules 559
8. Baer modules 562
9. Butler modules over valuation domains 570
10. Whitehead modules 576
Notes 582
Appendix on Set Theory 585
Bibliography 591
Author Index 603
Subject Index 607
|
| any_adam_object | 1 |
| author | Fuchs, László 1924- Salce, Luigi 1946- |
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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 |
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| id | DE-604.BV013416042 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:45:30Z |
| institution | BVB |
| isbn | 0821819631 9780821819630 |
| language | English |
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| physical | xiii, 613 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Fuchs, László 1924- Verfasser (DE-588)172083257 aut Modules over non-noetherian domains László Fuchs ; Luigi Salce Providence, Rhode Island American Mathematical Society [2001] © 2001 xiii, 613 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 84 Modul - Integritätsbereich Modul (DE-588)4129770-2 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Modul (DE-588)4129770-2 s Kommutativer Ring (DE-588)4164825-0 s DE-604 Salce, Luigi 1946- Verfasser (DE-588)1259081338 aut Erscheint auch als Online-Ausgabe 978-1-4704-1311-8 Mathematical surveys and monographs Volume 84 (DE-604)BV000018014 84 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009154436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fuchs, László 1924- Salce, Luigi 1946- Modules over non-noetherian domains Mathematical surveys and monographs Modul - Integritätsbereich Modul (DE-588)4129770-2 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4164825-0 |
| title | Modules over non-noetherian domains |
| title_auth | Modules over non-noetherian domains |
| title_exact_search | Modules over non-noetherian domains |
| title_full | Modules over non-noetherian domains László Fuchs ; Luigi Salce |
| title_fullStr | Modules over non-noetherian domains László Fuchs ; Luigi Salce |
| title_full_unstemmed | Modules over non-noetherian domains László Fuchs ; Luigi Salce |
| title_short | Modules over non-noetherian domains |
| title_sort | modules over non noetherian domains |
| topic | Modul - Integritätsbereich Modul (DE-588)4129770-2 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| topic_facet | Modul - Integritätsbereich Modul Kommutativer Ring |
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| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT fuchslaszlo modulesovernonnoetheriandomains AT salceluigi modulesovernonnoetheriandomains |