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Cogalois theory:

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Main Author:	Albu, Toma 1943- (Author)
Format:	Book
Language:	English
Published:	New York Marcel Dekker 2003
Series:	Pure and applied mathematics 252
Subjects:	Field extensions (Mathematics) Galois theory Galois-Theorie
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	XII, 341 S.
ISBN:	0824709497

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MARC


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adam_text	Contents PREFACE v INTRODUCTION 1 Part 1. FINITE COG ALOIS THEORY 13 Chapter 1. PRELIMINARIES 15 1.1. General notation and terminology 15 1.2. A short review of basic Field Theory 19 1.3. The Vahlen Capelli Criterion 39 1.4. Bounded Abelian groups 47 1.5. Exercises to Chapter 1 50 1.6. Bibliographical comments to Chapter 1 52 Chapter 2. KNESER EXTENSIONS 53 2.1. G Radical and G Kneser extensions 53 2.2. The Kneser Criterion 60 2.3. Exercises to Chapter 2 65 2.4. Bibliographical comments to Chapter 2 67 Chapter 3. COGALOIS EXTENSIONS 69 3.1. The Greither Harrison Criterion 69 3.2. Examples and properties of Cogalois extensions 74 3.3. The Cogalois group of a quadratic extension 83 3.4. Exercises to Chapter 3 86 3.5. Bibliographical comments to Chapter 3 88 Chapter 4. STRONGLY KNESER EXTENSIONS 89 4.1. Galois and Cogalois connections 90 4.2. Strongly G Kneser extensions 94 4.3. G Cogalois extensions 100 ix x Contents 4.4. The Kneser group of a G Cogalois extension 104 4.5. Almost G Cogalois extensions 108 4.6. Exercises to Chapter 4 120 4.7. Bibliographical comments to Chapter 4 123 Chapter 5. GALOIS G COGALOIS EXTENSIONS 125 5.1. Galois G radical extensions 125 5.2. Abelian G Cogalois extensions 128 5.3. Applications to elementary Field Arithmetic (I) 130 5.4. Exercises to Chapter 5 148 5.5. Bibliographical comments to Chapter 5 151 Chapter 6. RADICAL EXTENSIONS AND CROSSED HOMOMORPHISMS 153 6.1. Galois extensions and crossed homomorphisms 154 C.2. Radical extensions via crossed homomorphisms 159 G.3. Exercises to Chapter G 166 6.4. Bibliographical comments to Chapter 6 171 Chapter 7. EXAMPLES OF G COGALOIS EXTENSIONS 173 7.1. Classical Kummer extensions 173 7.2. Generalized Kummer extensions 178 7.3. Kummer extensions with few roots of unity 180 7.4. Quasi Kummer extensions 181 7.5. Cogalois extensions 184 7.6. Exercises to Chapter 7 186 7.7. Bibliographical comments to Chapter 7 189 Chapter 8. G COGALOIS EXTENSIONS AND PRIMITIVE ELEMENTS 191 8.1. Primitive elements for G Cogalois extensions 191 8.2. Applications to elementary Field Arithmetic (II) 196 8.3. Exercises to Chapter 8 204 8.4. Bibliographical comments to Chapter 8 205 Chapter 9. APPLICATIONS TO ALGEBRAIC NUMBER FIELDS 207 9.1. Number theoretic preliminaries 207 9.2. Some classical results via Cogalois Theory 212 9.3. Hecke systems of ideal numbers 218 Contents xi 9.4. Exercises to Chapter 9 225 9.5. Bibliographical comments to Chapter 9 227 Chapter 10. CONNECTIONS WITH GRADED ALGEBRAS AND HOPF ALGEBRAS 229 10.1. G Cogalois extensions via strongly graded fields 229 10.2. Cogalois extensions and Hopf algebras 242 10.3. Exercises to Chapter 10 253 10.4. Bibliographical comments to Chapter 10 255 Part 2. INFINITE COGALOIS THEORY 257 Chapter 11. INFINITE KNESER EXTENSIONS 259 11.1. Infinite G Kneser extensions 259 11.2. Infinite strongly Kneser extensions 262 11.3. Exercises to Chapter 11 266 11.4. Bibliographical comments to Chapter 11 267 Chapter 12. INFINITE G COGALOIS EXTENSIONS 269 12.1. The General Purity Criterion and its applications 269 12.2. Infinite Cogalois extensions 276 12.3. Exercises to Chapter 12 279 12.4. Bibliographical comments to Chapter 12 281 Chapter 13. INFINITE KUMMER THEORY 283 13.1. Infinite classical Kummer extensions 283 13.2. Infinite generalized Kummer extensions 285 13.3. Infinite Kummer extensions with few roots of unity 286 13.4. Infinite quasi Kummer extensions 287 13.5. Exercises to Chapter 13 289 13.6. Bibliographical comments to Chapter 13 289 Chapter 14. INFINITE GALOIS THEORY AND PONTRYAGIN DUALITY 291 14.1. Profinite groups and Infinite Galois Theory 291 14.2. Character group and Pontryagin Duality 296 14.3. Exercises to Chapter 14 300 14.4. Bibliographical comments to Chapter 14 303 xii Contents Chapter 15. INFINITE GALOIS G COGALOIS EXTENSIONS 305 15.1. The infinite Kneser group via crossed homomorphisms 306 15.2. Lattice isomorphic groups 314 15.3. Infinite Abelian (2 Cogalois extensions 317 15.4. Exercises to Chapter 15 325 15.5. Bibliographical comments to Chapter 15 327 Bibliography 329 Index 335
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illustrated	Not Illustrated
indexdate	2024-07-09T19:05:39Z
institution	BVB
isbn	0824709497
language	English
lccn	2002034849
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physical	XII, 341 S.
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series	Pure and applied mathematics
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spelling	Albu, Toma 1943- Verfasser (DE-588)128625440X aut Cogalois theory Toma Albu New York Marcel Dekker 2003 XII, 341 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 252 Includes bibliographical references and index Field extensions (Mathematics) Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s DE-604 Pure and applied mathematics 252 (DE-604)BV000001885 252 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009985691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Albu, Toma 1943- Cogalois theory Pure and applied mathematics Field extensions (Mathematics) Galois theory Galois-Theorie (DE-588)4155901-0 gnd
subject_GND	(DE-588)4155901-0
title	Cogalois theory
title_auth	Cogalois theory
title_exact_search	Cogalois theory
title_full	Cogalois theory Toma Albu
title_fullStr	Cogalois theory Toma Albu
title_full_unstemmed	Cogalois theory Toma Albu
title_short	Cogalois theory
title_sort	cogalois theory
topic	Field extensions (Mathematics) Galois theory Galois-Theorie (DE-588)4155901-0 gnd
topic_facet	Field extensions (Mathematics) Galois theory Galois-Theorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009985691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001885
work_keys_str_mv	AT albutoma cogaloistheory

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