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Field theory:

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Bibliographic Details
Main Author:	Roman, Steven (Author)
Format:	Book
Language:	English
Published:	New York u.a. Springer 1995
Series:	Graduate texts in mathematics 158
Subjects:	Körpertheorie Polynom Körper > Algebra Galois-Theorie Feldtheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 272 S.
ISBN:	0387944079 0387944087

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MARC


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Record in the Search Index

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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
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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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indexdate	2024-07-09T17:45:45Z
institution	BVB
isbn	0387944079 0387944087
language	English
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physical	XII, 272 S.
publishDate	1995
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publisher	Springer
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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
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT romansteven fieldtheory

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