Advanced modern algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Prentice Hall
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 1012 S., [14] Bl. |
| ISBN: | 0130878685 |
Staff View
MARC
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| 245 | 1 | 0 | |a Advanced modern algebra |c Joseph J. Rotman |
| 264 | 1 | |a Upper Saddle River, NJ |b Prentice Hall |c 2002 | |
| 300 | |a XV, 1012 S., [14] Bl. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Etymology xii
Special Notation xiii
Chapter 1 Things Past 1
1.1. Some Number Theory 1
1.2. Roots of Unity 15
1.3. Some Set Theory 25
Chapter 2 Groups I 39
2.1. Introduction 39
2.2. Permutations 40
2.3. Groups 51
2.4. Lagrange s Theorem 62
2.5. Homomorphisms 73
2.6. Quotient Groups 82
2.7. Group Actions 96
Chapter 3 Commutative Rings I 116
3.1. Introduction 116
3.2. First Properties 116
3.3. Polynomials 126
3.4. Greatest Common Divisors 131
3.5. Homomorphisms 143
3.6. Euclidean Rings 151
3.7. Linear Algebra 158
Vector Spaces 159
Linear Transformations 171
3.8. Quotient Rings and Finite Fields 182
vi Contents
Chapter 4 Fields 198
4.1. Insolvability of the Quintic 198
Formulas and Solvability by Radicals 206
Translation into Group Theory 210
4.2. Fundamental Theorem of Galois Theory 218
Chapter 5 Groups II 249
5.1. Finite Abelian Groups 249
Direct Sums 249
Basis Theorem 255
Fundamental Theorem 262
5.2. The Sylow Theorems 269
5.3. The Jordan Holder Theorem 278
5.4. Projective Unimodular Groups 289
5.5. Presentations 297
5.6. The Neilsen Schreier Theorem 311
Chapter 6 Commutative Rings II 319
6.1. Prime Ideals and Maximal Ideals 319
6.2. Unique Factorization Domains 326
6.3. Noetherian Rings 340
6.4. Applications of Zorn s Lemma 345
6.5. Varieties 375
6.6. Grobner Bases 399
Generalized Division Algorithm 400
Buchberger s Algorithm 411
Chapter 7 Modules and Categories 423
7.1. Modules 423
7.2. Categories 442
7.3. Functors 461
7.4. Free Modules, Projectives, and Injectives 471
7.5. Grothendieck Groups 488
7.6. Limits 498
Chapter 8 Algebras 520
8.1. Noncommutative Rings 520
8.2. Chain Conditions 533
8.3. Semisimple Rings 550
8.4. Tensor Products 574
8.5. Characters 605
8.6. Theorems of Burnside and of Frobenius 634
Contents vii
Chapter 9 Advanced Linear Algebra 646
9.1. Modules overPIDs 646
9.2. Rational Canonical Forms 666
9.3. Jordan Canonical Forms 675
9.4. Smith Normal Forms 682
9.5. Bilinear Forms 694
9.6. Graded Algebras 714
9.7. Division Algebras 727
9.8. Exterior Algebra 741
9.9. Determinants 756
9.10. Lie Algebras 772
Chapter 10 Homology 781
10.1. Introduction 781
10.2. Semidirect Products 784
10.3. General Extensions and Cohomology 794
10.4. Homology Functors 813
10.5. Derived Functors 830
10.6. Ext and Tor 852
10.7. Cohomology of Groups 870
10.8. Crossed Products 887
10.9. Introduction to Spectral Sequences 893
Chapter 11 Commutative Rings III 898
11.1. Local and Global 898
11.2. Dedekind Rings 922
Integrality 923
Nullstellensatz Redux 931
Algebraic Integers 938
Characterizations of Dedekind Rings 948
Finitely Generated Modules over Dedekind Rings 959
11.3. Global Dimension 969
11.4. Regular Local Rings 985
Appendix The Axiom of Choice and Zorn s Lemma A i
Bibliography B l
Index I l
|
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| author | Rotman, Joseph J. 1934- |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:15Z |
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| isbn | 0130878685 |
| language | English |
| lccn | 2002017072 |
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| physical | XV, 1012 S., [14] Bl. |
| publishDate | 2002 |
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| publishDateSort | 2002 |
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| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut Advanced modern algebra Joseph J. Rotman Upper Saddle River, NJ Prentice Hall 2002 XV, 1012 S., [14] Bl. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Algebra Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009848447&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotman, Joseph J. 1934- Advanced modern algebra Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | Advanced modern algebra |
| title_auth | Advanced modern algebra |
| title_exact_search | Advanced modern algebra |
| title_full | Advanced modern algebra Joseph J. Rotman |
| title_fullStr | Advanced modern algebra Joseph J. Rotman |
| title_full_unstemmed | Advanced modern algebra Joseph J. Rotman |
| title_short | Advanced modern algebra |
| title_sort | advanced modern algebra |
| topic | Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra |
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