Field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1995
|
| Schriftenreihe: | Graduate texts in mathematics
158 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 272 S. |
| ISBN: | 0387944079 0387944087 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804124443874689024 |
|---|---|
| adam_text | STEVEN ROMAN
FIELD THEOR
Y
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO HONG KONG BARCELONA BUDAPEST
CONTENTS
SECTIONS MARKED WITH AN ASTERISK ARE OPTIONAL.
PREFACE VII
CHAPTER 0
PRELIMINARIES 1
0.1 LATTICES 1
0.2 GROUPS 3
0.3 RINGS 12
0.4 INTEGRAL DOMAINS 15
0.5 UNIQUE FACTORIZATION DOMAINS 17
0.6 PRINCIPAL IDEAL DOMAINS 17
0.7 EUCLIDEAN DOMAINS 18
0.8 TENSOR PRODUCTS 19
PAR
T 1 BASIC THEORY 23
CHAPTER 1
POLYNOMIALS 25
1.1 POLYNOMIALS OVER A RING 25
1.2 PRIMITIVE POLYNOMIALS 26
1.3 THE DIVISION ALGORITHM 28
1.4 SPLITTING FIELDS 31
1.5 TH
E MINIMAL POLYNOMIAL 32
1.6 MULTIPLE ROOTS 33
1.7 TESTING FOR IRREDUCIBILITY 35
: CONTENT
S
CHAPTER 2
FIELD EXTENSIONS 3
9
2.1 THE LATTICE OF SUBFIELDS OF A FIELD 39
2.2 DISTINGUISHED EXTENSIONS 40
2.3 FINITELY GENERATED EXTENSIONS 41
2.4 SIMPLE EXTENSIONS 42
2.5 FINITE EXTENSIONS 43
2.6 ALGEBRAIC EXTENSIONS 45
2.7 ALGEBRAIC CLOSURES 46
2.8 EMBEDDINGS 48
2.9 SPLITTING FIELDS AND NORMAL EXTENSIONS 52
CHAPTER 3
ALGEBRAIC INDEPENDENCE 6
1
3.1 DEPENDENCE RELATIONS 61
3.2 ALGEBRAIC DEPENDENCE 64
3.3 TRANSCENDENCE BASES 67
*3.4 SIMPLE TRANSCENDENTAL EXTENSIONS 73
CHAPTER 4
SEPARABILITY 79
4.1 SEPARABLE POLYNOMIALS 79
4.2 SEPARABLE DEGREE 81
4.3 THE SIMPLE CASE 82
4.4 THE FINITE CASE 84
4.5 TH
E ALGEBRAIC CASE 87
4.6 PURE INSEPARABILITY
L
88
4.7 SEPARABLE AND PURELY INSEPARABLE CLOSURES 91
4.8 PERFECT FIELDS 94
PART 2 GALOIS THEORY 99
CHAPTER 5
GALOIS THEORY I
5.1 GALOIS CONNECTIONS
5.2 THE GALOIS CORRESPONDENCE
5.3 WHO S CLOSED?
5.4 NORMAL SUBGROUPS AND NORMAL EXTENSIONS
5.5 MORE ON GALOIS GROUPS
101
101
104
109
112
113
CONTENTS
*5.6 LINEAR DISJOINTNESS 117
*5.7 THE KRULL TOPOLOGY 120
CHAPTER 6
GALOIS THEORY II 127
6.1 THE GALOIS GROUP OF A POLYNOMIAL 127
6.2 SYMMETRIC POLYNOMIALS 128
6.3 THE DISCRIMINANT OF A POLYNOMIAL 132
6.4 THE GALOIS GROUPS OF SOME SMALL DEGREE POLYNOMIALS 134
CHAPTER 7
A FIELD EXTENSION AS A VECTOR SPACE 147
7.1 THE NORM AND TH
E TRACE 147
*7.2 THE DISCRIMINANT OF FIELD ELEMENTS 151
*7.3 ALGEBRAIC INDEPENDENCE OF EMBEDDINGS 155
*7.4 THE NORMAL BASIS THEOREM 156
CHAPTER 8
FINITE FIELDS I: BASIC PROPERTIES 161
8.1 FINITE FIELDS 161
8.2 FINITE FIELDS AS SPLITTING FIELDS 162
8.3 THE SUBFIELDS OF A FINITE FIELD 163
8.4 THE MULTIPLICATIVE STRUCTURE OF A FINITE FIELD 163
8.5 THE GALOIS GROUP OF A FINITE FIELD 165
8.6 IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS 165
*8.7 NORMAL BASES 169
*8.8 THE ALGEBRAIC CLOSURE OF A FINITE FIELD 170
CHAPTER 9
FINITE FIELDS II: ADDITIONAL PROPERTIES 175
9.1 FINITE FIELD ARITHMETIC 175
*9.2 THE NUMBER OF IRREDUCIBLE POLYNOMIALS 178
*9.3 POLYNOMIAL FUNCTIONS 180
*9.4 LINEARIZED POLYNOMIALS 182
|
| any_adam_object | 1 |
| author | Roman, Steven |
| author_facet | Roman, Steven |
| author_role | aut |
| author_sort | Roman, Steven |
| author_variant | s r sr |
| building | Verbundindex |
| bvnumber | BV010059656 |
| classification_rvk | SK 230 |
| classification_tum | MAT 120f |
| ctrlnum | (OCoLC)844947306 (DE-599)BVBBV010059656 |
| dewey-full | 512.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.3 |
| dewey-search | 512.3 |
| dewey-sort | 3512.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010059656 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:45Z |
| institution | BVB |
| isbn | 0387944079 0387944087 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006673967 |
| oclc_num | 844947306 |
| open_access_boolean | |
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| physical | XII, 272 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Roman, Steven Verfasser aut Field theory Steven Roman New York u.a. Springer 1995 XII, 272 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 158 Körpertheorie (DE-588)4164455-4 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Körper Algebra (DE-588)4308063-7 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Körpertheorie (DE-588)4164455-4 s DE-188 Körper Algebra (DE-588)4308063-7 s Feldtheorie (DE-588)4016698-3 s Galois-Theorie (DE-588)4155901-0 s 1\p DE-604 Polynom (DE-588)4046711-9 s 2\p DE-604 Graduate texts in mathematics 158 (DE-604)BV000000067 158 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006673967&sequence=000001&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 |
| spellingShingle | Roman, Steven Field theory Graduate texts in mathematics Körpertheorie (DE-588)4164455-4 gnd Polynom (DE-588)4046711-9 gnd Körper Algebra (DE-588)4308063-7 gnd Galois-Theorie (DE-588)4155901-0 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4164455-4 (DE-588)4046711-9 (DE-588)4308063-7 (DE-588)4155901-0 (DE-588)4016698-3 |
| title | Field theory |
| title_auth | Field theory |
| title_exact_search | Field theory |
| title_full | Field theory Steven Roman |
| title_fullStr | Field theory Steven Roman |
| title_full_unstemmed | Field theory Steven Roman |
| title_short | Field theory |
| title_sort | field theory |
| topic | Körpertheorie (DE-588)4164455-4 gnd Polynom (DE-588)4046711-9 gnd Körper Algebra (DE-588)4308063-7 gnd Galois-Theorie (DE-588)4155901-0 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Körpertheorie Polynom Körper Algebra Galois-Theorie Feldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006673967&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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