Holdings: Factorization :: THWS Bibkatalog

Factorization: unique and otherwise

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Bibliographic Details
Main Author:	Weintraub, Steven H. 1951- (Author)
Format:	Book
Language:	English
Published:	Ottawa, Ont Canadian Mathematical Society/Société mathématique du Canada 2008
Series:	CMS treatises in mathematics
Online Access:	Inhaltsverzeichnis
Item Description:	Includes index
Physical Description:	X, 260 S. graph. Darst.
ISBN:	9781568812410

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MARC


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adam_text	Titel: Factorization Autor: Weintraub, Steven H Jahr: 2008 Contents Preface ix Introduction 1 1 Basic Notions 7 1.1 Integral Domains....................... 7 1.2 Quadratic Fields....................... 12 1.3 Exercises ........................... 16 2 Unique Factorization 19 2.1 Euclidean Domains...................... 20 2.2 The GCD-L Property and Euclid s Algorithm....... 31 2.3 Ideals and Principal Ideal Domains............. 45 2.4 Unique Factorization Domains ............... 51 2.5 Nonunique Factorization: The Case D 0......... 60 2.6 Nonunique Factorization: The Case D 0......... 67 2.7 Summing Up......................... 78 2.8 Exercises ........................... 80 3 The Gaussian Integers 91 3.1 Fermat s Theorem...................... 92 3.2 Factorization into Primes.................. 101 3.3 Exercises ........................... 105 4 Pell s Equation 111 4.1 Representations and Their Composition.......... 112 4.2 Solving Pell s Equation.................... 118 4.3 Numerical Examples and Further Results......... 127 4.4 Units in 0(^/D) ....................... 137 4.5 Exercises ........................... 139 viii Contents 5 Towards Algebraic Number Theory 143 5.1 Algebraic Numbers and Algebraic Integers......... 144 5.2 Ideal Theory ......................... 147 5.3 Dedekind Domains...................... 150 5.4 Algebraic Number Fields and Dedekind Domains..... 154 5.5 Prime Ideals in 0(y/D) ................... 158 5.6 Examples of Ideals in 0(773)................ 166 5.7 Behavior of Ideals in Algebraic Number Fields ...... 178 5.8 Ideal Elements........................ 180 5.9 Dirichlet s Unit Theorem .................. 182 5.10 Exercises ........................... 186 A Mathematical Induction 191 A.l Mathematical Induction and Its Equivalents........ 191 A.2 Consequences of Mathematical Induction ......... 196 A.3 Exercises ........................... 199 B Congruences 205 B.l The Notion of Congruence.................. 205 B.2 Linear Congruences...................... 211 B.3 Quadratic Congruences ................... 223 B.4 Proof of the Law of Quadratic Reciprocity......... 236 B.5 Primitive Roots........................ 241 B.6 Exercises ........................... 245 C Continuations from Chapter 2 251 C.l Continuation of the Proof of Theorem 2.8......... 251 C.2 Continuation of Example 2.26................ 255 C.3 Exercises ........................... 257 Index 259
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spelling	Weintraub, Steven H. 1951- Verfasser (DE-588)113001770 aut Factorization unique and otherwise Steven H. Weintraub Ottawa, Ont Canadian Mathematical Society/Société mathématique du Canada 2008 X, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CMS treatises in mathematics Includes index HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018593848&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Weintraub, Steven H. 1951- Factorization unique and otherwise
title	Factorization unique and otherwise
title_auth	Factorization unique and otherwise
title_exact_search	Factorization unique and otherwise
title_full	Factorization unique and otherwise Steven H. Weintraub
title_fullStr	Factorization unique and otherwise Steven H. Weintraub
title_full_unstemmed	Factorization unique and otherwise Steven H. Weintraub
title_short	Factorization
title_sort	factorization unique and otherwise
title_sub	unique and otherwise
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018593848&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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