Noncommutative Noetherian rings:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2001
|
| Edition: | printed with corrections |
| Series: | Graduate studies in mathematics
Volume 30 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 636 Seiten |
| ISBN: | 9780821821695 0821821695 |
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MARC
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| 100 | 1 | |a McConnell, John C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Noncommutative Noetherian rings |c J. C. McConnell, J. C. Robson ; with the cooperation of L.W. Small |
| 250 | |a printed with corrections | ||
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2001 | |
| 300 | |a XX, 636 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate studies in mathematics |v Volume 30 | |
| 650 | 0 | 7 | |a Noetherscher Ring |0 (DE-588)4171970-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtkommutativer Ring |0 (DE-588)4246997-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtkommutativer Ring |0 (DE-588)4246997-1 |D s |
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| 700 | 1 | |a Robson, James C. |d 1940- |e Verfasser |0 (DE-588)17233425X |4 aut | |
| 700 | 1 | |a Small, L.W. |e Sonstige |4 oth | |
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Record in the Search Index
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| adam_text |
Contents
Preface to the Revised Edition xiii
Preface xv
Notation xix
Chapter 0. Preliminaries 1
§1. Chain Conditions 1
§2. Prime Radical 4
§3. Jacobson Radical 6
Part I. Basic Theory
Chapter 1. Some Noetherian Rings 11
§1. Matrices 11
§2. Skew Polynomial Rings 15
§3. Weyl Algebras 19
§4. Skew Power Series and Laurent Polynomials 21
§5. Group Rings and Generalizations 22
§6. Skew Polynomial Rings in Several Variables 26
§7. Enveloping Algebras and Their Generalizations 30
§8. Further Simple Rings 35
vii
§9. Additional Remarks 38
Chapter 2. Quotient Rings and Goldie's Theorem 41
§1. Right Quotient Rings 41
§2. Uniform Dimension 51
§3. Goldie's Theorem 57
§4. Additional Remarks 62
Chapter 3. Structure of Semiprime Goldie Rings 63
§1. Orders in Quotient Rings 63
§2. Minimal Primes 70
§3. Right Ideals in Semiprime Rings 74
§4. Endomorphism Rings 78
§5. Morita Equivalence 83
§6. Morita Contexts and Prime Rings 89
§7. Additional Remarks 94
Chapter 4. Semiprime Ideals in Noetherian Rings 97
§1. Reduced Rank and Applications 98
§2. Artin Rees Property and Localization 106
§3. Localization and Prime Ideals 112
§4. Affiliated Primes and Regular Elements 123
§5. Additivity 128
§6. Patch Continuity 131
§7. Additional Remarks 138
Chapter 5. Some Dedekind like Rings 141
§1. Maximal Orders 142
§2. Asano and Dedekind Prime Rings 146
§3. Classical Orders 152
§4. Hereditary Noetherian Rings 159
§5. Idealizer Rings 162
§6. Hereditary Noetherian Prime Rings 166
§7. Modules over Dedekind Prime Rings 172
§8. Additional Remarks 180
Part II. Dimensions
Chapter 6. Krull Dimension 185
§1. Deviation of a Poset 186
§2. Krull Dimension of Modules 192
§3. Krull Dimension in Rings 200
§4. Prime Ideals and FBN Rings 204
§5. Bounds on Krull Dimensions 209
§6. Calculation of Krull Dimension 213
§7. Stable Bounds on Generators 219
§8. Quotient Rings and Localization 223
§9. Skew Polynomials over Commutative Rings 233
§10. Additional Remarks 242
Chapter 7. Global Dimension 245
§1. Preliminaries 245
§2. Change of Rings 250
§3. Factor Rings 253
§4. Localization 260
§5. Estimates of Global Dimension 261
§6. Filtered and Graded Modules 270
§7. Regular Rings 275
§8. Fixed Rings 278
§9. Skew Polynomial Rings 282
§10. Skew Polynomials over Commutative Rings 290
§11. Simple Dedekind Domains 291
§12. Additional Remarks 294
Chapter 8. Gelfand Kirillov Dimension 297
§1. Definition and Examples 298
§2. Dimensions of Related Algebras 304
§3. Module Theory 311
§4. Almost Commutative Algebras and Hilbert Polynomials 320
§5. Applications 324
§6. Somewhat Commutative Algebras 330
§7. Additional Remarks 337
Part III. Extensions
Chapter 9. The Nullstellensatz 341
§1. Algebras over a Field 341
§2. Algebras over Rings 346
§3. Generic Flatness 348
§4. Constructible Algebras 351
§5. Finite Dimensional Endomorphism Rings 356
§6. Polynomials over Division Rings 358
§7. Additional Remarks 362
Chapter 10. Prime Ideals in Extension Rings 365
§1. Finite Extensions and Chain Conditions 366
§2. Prime Ideals 370
§3. Quotient Rings and Closure 375
§4. Incomparability 380
§5. Crossed Products and Fixed Rings 387
§6. Primes in Polynomial Rings 392
§7. Additional Remarks 400
Chapter 11. Stability 403
§1. Stably Free Modules 404
§2. Stably Free Nonfree Modules 409
§3. Stable and Elementary Ranks 413
§4. Cancellation of Modules 418
§5. Ranks of Certain Rings 421
§6. Local Information 428
§7. Stability and Cancellation 435
§8. Additional Remarks 443
Chapter 12. Kq and Extension Rings 445
§1. Ko of a Ring 446
§2. Projective Graded Modules 449
§3. Filtrations and the Syzygy Theorem 453
§4. Kq of Module Categories 456
§5. Skew Laurent Extensions 461
§6. Filtered Rings 463
§7. Applications to Simple Rings 467
§8. Additional Remarks 472
Part IV. Examples
Chapter 13. Polynomial Identity Rings 477
§1. Polynomial Identities 478
§2. Nilpotence 484
§3. Central Simple Algebras 486
§4. Embeddings and Matrix Rings 489
§5. Central Polynomials 492
§6. Semiprime Rings and Central Polynomials 497
§7. Prime Ideals and Azumaya Algebras 501
§8. Integral Extensions and Prime Rings 507
§9. The Trace Ring and Maximal Orders 514
§10. Affine fc algebras 518
§11. Additional Remarks 523
Chapter 14. Enveloping Algebras of Lie Algebras 525
§1. Basics 526
§2. Prime Ideals 530
§3. Eigenvalues and Prime Ideals 534
§4. Primitive Ideals 537
§5. The Solvable Case 542
§6. When Eigenvectors are Central 545
§7. When g is Algebraic 550
§8. The Simple Algebras A(V, 6, T) 552
§9. The General Case 557
§10. Additional Remarks 563
Chapter 15. Rings of Differential Operators on Algebraic Varieties 565
§1. Algebras over a Ring 566
§2. Affine Algebras over a Field 573
§3. Dimensions 578
§4. Further Properties 585
§5. Rings of Differential Operators 590
§6. Additional Remarks 593
References 595
Index of Notation 621
Index 625 |
| any_adam_object | 1 |
| author | McConnell, John C. Robson, James C. 1940- |
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| ctrlnum | (OCoLC)633377824 (DE-599)BVBBV017337411 |
| discipline | Mathematik |
| edition | printed with corrections |
| format | Book |
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| language | English |
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| physical | XX, 636 Seiten |
| publishDate | 2001 |
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| publisher | American Mathematical Society |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | McConnell, John C. Verfasser aut Noncommutative Noetherian rings J. C. McConnell, J. C. Robson ; with the cooperation of L.W. Small printed with corrections Providence, Rhode Island American Mathematical Society 2001 XX, 636 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics Volume 30 Noetherscher Ring (DE-588)4171970-0 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 s Noetherscher Ring (DE-588)4171970-0 s DE-604 Robson, James C. 1940- Verfasser (DE-588)17233425X aut Small, L.W. Sonstige oth Erscheint auch als Online-Ausgabe 978-1-4704-2084-0 Graduate studies in mathematics Volume 30 (DE-604)BV009739289 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010453755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McConnell, John C. Robson, James C. 1940- Noncommutative Noetherian rings Graduate studies in mathematics Noetherscher Ring (DE-588)4171970-0 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| subject_GND | (DE-588)4171970-0 (DE-588)4246997-1 |
| title | Noncommutative Noetherian rings |
| title_auth | Noncommutative Noetherian rings |
| title_exact_search | Noncommutative Noetherian rings |
| title_full | Noncommutative Noetherian rings J. C. McConnell, J. C. Robson ; with the cooperation of L.W. Small |
| title_fullStr | Noncommutative Noetherian rings J. C. McConnell, J. C. Robson ; with the cooperation of L.W. Small |
| title_full_unstemmed | Noncommutative Noetherian rings J. C. McConnell, J. C. Robson ; with the cooperation of L.W. Small |
| title_short | Noncommutative Noetherian rings |
| title_sort | noncommutative noetherian rings |
| topic | Noetherscher Ring (DE-588)4171970-0 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| topic_facet | Noetherscher Ring Nichtkommutativer Ring |
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