Algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menlo Park, Calif. u.a.
Addison-Wesley
1984
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 714 S. |
| ISBN: | 0201054876 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804119978515890176 |
|---|---|
| adam_text | CONTENTS
Part One Groups, Rings, and Modules
Chapter I Groups 3
1. Monoids 3
2. Groups 7
3. Cyclic groups 11
4. Normal subgroups 12
5. Operations of a group on a set 20
6. Sylow subgroups 24
7. Categories and functors 26
8. Free groups 34
9. Direct sums and free abelian groups 41
10. Finitely generated abelian groups 47
11. The dual group 51
Chapter II Rings 60
1. Rings and homomorphisms 60
2. Commutative rings 66
3. Localization 71
4. Principal rings 74
5. Spec of a ring 77
Chapter III Modules 81
1. Basic definitions 81
2. The group of homomorphisms 84
3. Direct products and sums of modules 86
4. Free modules 92
5. Vector spaces 93
6. The dual space 96
7. The snake lemma 100
xi
8. Projective and injective modules 101
9. Direct and inverse limits 106
Chapter IV Homology 116
1. Complexes 117
2. Homology sequence 121
3. Euler characteristic 123
4. Special complexes 133
5. Homotopies of morphisms of complexes 137
6. Derived functors 141
7. Delta functors 148
8. Bifunctors 155
9. Spectral sequences 163
Chapter V Polynomials 176
1. Free algebras 176
2. Definition of polynomials 180
3. Elementary properties of polynomials 185
4. The Euclidean algorithm 190
5. Partial fractions 194
6. Unique factorization in several variables 197
7. Criteria for irreducibility 200
8. The derivative and multiple roots 202
9. Symmetric polynomials 204
10. The resultant 206
11. Power series 211
Chapter VI Noetherian Rings and Modules 222
1. Basic criteria 222
2. Hilbert s theorem 226
3. Power series are Noetherian 227
4. Associated primes 228
5. Primary decomposition 233
6. Nakayama s lemma 236
7. Filtered and graded modules 238
8. The Hilbert polynomial 243
9. Indecomposable modules 246
10. Finite free resolutions 250
Part Two Field Theory
Chapter VII Algebraic Extensions 265
1. Finite and algebraic extensions 265
2. Algebraic closure 271
3. Splitting fields and normal extensions 278
4. Separable extensions 281
5. Finite fields 287
6. Primitive elements 290
7. Purely inseparable extensions 291
Chapter VIII Galois Theory 300
1. Galois extensions 300
2. Examples and applications 308
3. Roots of unity 313
4. Linear independence of characters 318
5. The norm and trace 320
6. Cyclic extensions 323
7. Solvable and radical extensions 326
8. Abelian Kummer theory 328
9. The equation X a = 0 331
10. Galois cohomology 334
11. Non abelian Kummer extensions 336
12. Algebraic independence of homomorphisms 340
13. The normal basis theorem 344
Chapter IX Extensions of Rings 355
1. Integral ring extensions 355
2. Integral Galois extensions 362
3. Extension of homomorphisms 368
Chapter X Transcendental Extensions 372
1. Transcendence bases 372
2. Hilbert s Nullstellensatz 374
3. Algebraic sets 376
4. Noether normalization theorem 378
5. Linearly disjoint extensions 379
6. Separable extensions 382
7. Derivations 385
Chapter XI Real Fields 390
1. Ordered fields 390
2. Real fields 392
3. Real zeros and homomorphisms 398
Chapter XII Absolute Values 404
1. Definitions, dependence, and independence 404
2. Completions 407
3. Finite extensions 414
4. Valuations 417
5. Completions and valuations 425
6. Discrete valuations 426
7. Zeros of polynomials in complete fields 430
Part Three Linear Algebra and Representations
Chapter XIII Matrices and Linear Maps 441
1. Matrices 441
2. The rank of a matrix 444
3. Matrices and linear maps 445
4. Determinants 449
5. Duality 458
6. Matrices and bilinear forms 463
7. Sesquilinear duality 467
8. The simplicity of SL2(F)/±1 472
9. The group SLn(F), n 3 476
10. Fitting ideals 480
11. Unimodular polynomial vectors 488
Chapter XIV Structure of Bilinear Forms 498
1. Preliminaries, orthogonal sums 498
2. Quadratic maps 501
3. Symmetric forms, orthogonal bases 502
4. Hyperbolic spaces 503
5. Witt s theorem 505
6. The Witt group 508
7. Symmetric forms over ordered fields 509
8. The Clifford algebra 511
9. Alternating forms 515
10. ThePfafnan 517
11. Hermitian forms 519
12. The spectral theorem (hermitian case) 521
13. The spectral theorem (symmetric case) 524
Chapter XV Representation of One Endomorphism 529
1. Representations 529
2. Modules over principal rings 532
3. Decomposition over one endomorphism 541
4. The characteristic polynomial 545
Chapter XVI Multilinear Products 554
1. Tensor product 554
2. Basic properties 560
3. Flat modules 565
4. Extension of the base 575
5. Some functorial isomorphisms
6. Tensor product of algebras 581
7. The tensor algebra of a module 583
8. Symmetric products 586
9. Alternating products 588
10. The Koszul complex 593
11. The Grothendieck ring 605
12. Universal derivations 610
Chapter XVII Semisimplicity 621
1. Matrices and linear maps over non commutative rings 621
2. Conditions denning semisimplicity 625
3. The density theorem 626
4. Semisimple rings 629
5. Simple rings 632
6. Balanced modules 636
Chapter XVIII Representations of Finite Groups 639
1. Semisimplicity of the group algebra 639
2. Characters 641
3. 1 dimensional representations 645
4. The space of class functions 647
5. Orthogonality relations 651
6. Induced characters 659
7. Induced representations 661
8. Positive decomposition of the regular character 666
9. Supersolvable groups 668
10. Brauer s theorem 671
11. Field of definition of a representation 674
Appendix 1 The Transcendence of e and n 681
Appendix 2 Some Set Theory 688
Index 707
|
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| callnumber-first | Q - Science |
| callnumber-label | QA154 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 |
| ctrlnum | (OCoLC)10727130 (DE-599)BVBBV005794205 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV005794205 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:34:47Z |
| institution | BVB |
| isbn | 0201054876 |
| language | English |
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| physical | XV, 714 S. |
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| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Algebra 2. ed. Menlo Park, Calif. u.a. Addison-Wesley 1984 XV, 714 S. txt rdacontent n rdamedia nc rdacarrier Algebra gtt Algebra (DE-588)4001156-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content 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=003620869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Algebra |
| title_auth | Algebra |
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