Further algebra and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Ausg. u.d.T.: Cohn, P. M.: Algebra |
| Physical Description: | XI, 451 S. graph. Darst. |
| ISBN: | 1852336676 |
Staff View
MARC
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| 245 | 1 | 0 | |a Further algebra and applications |c P. M. Cohn |
| 264 | 1 | |a London [u.a.] |b Springer |c 2003 | |
| 300 | |a XI, 451 S. |b graph. Darst. | ||
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| 500 | |a Frühere Ausg. u.d.T.: Cohn, P. M.: Algebra | ||
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Record in the Search Index
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| adam_text | Contents
Conventions on Terminology ix
Preface xi
1. Universal algebra
1.1 Algebras and homomorphisms 1
1.2 Congruences and the isomorphism theorems 4
1.3 Free algebras and varieties 11
1.4 The diamond lemma 18
1.5 Ultraproducts 20
1.6 The natural numbers 24
2. Homological algebra
2.1 Additive and abelian categories 33
2.2 Functors on abelian categories 41
2.3 The category Mod« 50
2.4 Homological dimension 56
2.5 Derived functors 61
2.6 Ext, Tor and global dimension 72
2.7 Tensor algebras, universal derivations and syzygies 78
3. Further group theory
3.1 Group extensions 91
3.2 Hall subgroups 102
3.3 The transfer 107
3.4 Free groups 109
3.5 Linear groups 116
3.6 The symplectic group 121
3.7 The orthogonal group 126
4. Algebras
4.1 The Krull Schmidt theorem 135
4.2 The protective cover of a module 139
4.3 Semiperfect rings 142
v
vi Further Algebra and Applications
4.4 Equivalence of module categories 148
4.5 The Morita context 155
4.6 Protective, injective and flat modules 160
4.7 Hochschild cohomology and separable algebras 168
5. Central simple algebras
5.1 Simple Artinian rings 179
5.2 The Brauer group 187
5.3 The reduced norm and trace 194
5.4 Quaternion algebras 200
5.5 Crossed products 203
5.6 Change of base field 209
5.7 Cyclic algebras 215
6. Representation theory of finite groups
6.1 Basic definitions 221
6.2 The averaging lemma and Maschke s theorem 226
6.3 Orthogonality and completeness 229
6.4 Characters 233
6.5 Complex representations 241
6.6 Representations of the symmetric group 247
6.7 Induced representations 253
6.8 Applications: The theorems of Burnside and Frobenius 259
7. Noetherian rings and polynomial identities
7.1 Rings of fractions 265
7.2 Principal ideal domains 271
7.3 Skew polynomial rings and Laurent series 274
7.4 Goldie s theorem 282
7.5 Pi algebras 290
7.6 Varieties of Pi algebras and Regev s theorem 295
7.7 Generic matrix rings and central polynomials 299
7.8 Generalized polynomial identities 303
8. Rings without finiteness assumptions
8.1 The density theorem revisited 309
8.2 Primitive rings 315
8.3 Semiprimitive rings and the lacobson radical 318
8.4 Non unital algebras 322
8.5 Semiprime rings and nilradicals 328
8.6 Prime Pi algebras 334
8.7 Firs and semifirs 337
9. Skew fields
9.1 Generalities 343
9.2 The Dieudonne determinant 346
Contents vii
9.3 Free fields 354
9.4 Valuations on skew fields 358
9.5 Pseudo linear extensions 365
10. Coding theory
10.1 The transmission of information 371
10.2 Block codes 373
10.3 Linear codes 376
10.4 Cyclic codes 384
10.5 Other codes 389
11. Languages and automata
11.1 Monoids and monoid actions 395
11.2 Languages and grammars 399
11.3 Automata 403
11.4 Variable length codes 411
11.5 Free algebras and formal power series rings 419
Bibliography 431
List of Notations 437
Author Index 441
Subject Index 445
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| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
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| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T19:07:34Z |
| institution | BVB |
| isbn | 1852336676 |
| language | English |
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| physical | XI, 451 S. graph. Darst. |
| publishDate | 2003 |
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| spelling | Cohn, Paul M. 1924-2006 Verfasser (DE-588)121230538 aut Further algebra and applications P. M. Cohn London [u.a.] Springer 2003 XI, 451 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frühere Ausg. u.d.T.: Cohn, P. M.: Algebra Algèbre Álgebra abstrata larpcal Álgebra larpcal 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=010026850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohn, Paul M. 1924-2006 Further algebra and applications Algèbre Álgebra abstrata larpcal Álgebra larpcal Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | Further algebra and applications |
| title_auth | Further algebra and applications |
| title_exact_search | Further algebra and applications |
| title_full | Further algebra and applications P. M. Cohn |
| title_fullStr | Further algebra and applications P. M. Cohn |
| title_full_unstemmed | Further algebra and applications P. M. Cohn |
| title_short | Further algebra and applications |
| title_sort | further algebra and applications |
| topic | Algèbre Álgebra abstrata larpcal Álgebra larpcal Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algèbre Álgebra abstrata Álgebra Algebra |
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