Field and Galois theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1996
|
| Series: | Graduate texts in mathematics
167 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 281 S. graph. Darst. |
| ISBN: | 0387947531 9781461284758 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Notes to the Reader ix
List of Symbols xiii
I Galois Theory 1
1 Field Extensions 1
2 Automorphisms 15
3 Normal Extensions 27
4 Separable and Inseparable Extensions 39
5 The Fundamental Theorem of Galois Theory 51
II Some Galois Extensions 65
6 Finite Fields 65
7 Cyclotomic Extensions 71
8 Norms and Traces 78
9 Cyclic Extensions 87
10 Hilbert Theorem 90 and Group Cohomology 93
11 Kummer Extensions 104
III Applications of Galois Theory 111
12 Discriminants 112
13 Polynomials of Degree 3 and 4 123
xii Contents
14 The Transcendence of it and e 133
15 Ruler and Compass Constructions 140
16 Solvability by Radicals 147
IV Infinite Algebraic Extensions 155
17 Infinite Galois Extensions 155
18 Some Infinite Galois Extensions 164
V Transcendental Extensions 173
19 Transcendence Bases 173
20 Linear Disjointness 182
21 Algebraic Varieties 192
22 Algebraic Function Fields 201
23 Derivations and Differentials 210
Appendix A Ring Theory 225
1 Prime and Maximal Ideals 226
2 Unique Factorization Domains 227
3 Polynomials over a Field 230
4 Factorization in Polynomial Rings 232
5 Irreducibility Tests 234
Appendix B Set Theory 241
1 Zorn s Lemma 241
2 Cardinality and Cardinal Arithmetic 243
Appendix C Group Theory 245
1 Fundamentals of Finite Groups 245
2 The Sylow Theorems 247
3 Solvable Groups 248
4 Profinite Groups 249
Appendix D Vector Spaces 255
1 Bases and Dimension 255
2 Linear Transformations 257
3 Systems of Linear Equations and Determinants 260
4 Tensor Products 261
Appendix E Topology 267
1 Topological Spaces 267
2 Topological Properties 270
References 275
Index 277
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T18:02:33Z |
| institution | BVB |
| isbn | 0387947531 9781461284758 |
| language | German |
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| physical | XVI, 281 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Morandi, Patrick J. Verfasser (DE-588)1058345249 aut Field and Galois theory Patrick Morandi New York [u.a.] Springer 1996 XVI, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 167 Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Körpertheorie (DE-588)4164455-4 s DE-604 Galois-Theorie (DE-588)4155901-0 s Erscheint auch als Online-Ausgabe 978-1-4612-4040-2 Graduate texts in mathematics 167 (DE-604)BV000000067 167 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007371415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morandi, Patrick J. Field and Galois theory Graduate texts in mathematics Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd Körpertheorie (DE-588)4164455-4 gnd |
| subject_GND | (DE-588)4155901-0 (DE-588)4164455-4 |
| title | Field and Galois theory |
| title_auth | Field and Galois theory |
| title_exact_search | Field and Galois theory |
| title_full | Field and Galois theory Patrick Morandi |
| title_fullStr | Field and Galois theory Patrick Morandi |
| title_full_unstemmed | Field and Galois theory Patrick Morandi |
| title_short | Field and Galois theory |
| title_sort | field and galois theory |
| topic | Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd Körpertheorie (DE-588)4164455-4 gnd |
| topic_facet | Algebraic fields Galois theory Galois-Theorie Körpertheorie |
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