Fundamentals of modern algebra: a global perspective
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | x, 220 Seiten Illustrationen 24 cm |
| ISBN: | 9789814730297 9789814730280 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804176398835777536 |
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| adam_text | Titel: Fundamentals of modern algebra
Autor: Underwood, Robert G
Jahr: 2016
Contents
Preface vii
1. Groups 1
1.1 Introduction to Groups........................................1
1.2 Subgroups......................................................11
1.3 Homomorphisms of Groups..................................16
1.4 Group Structure ..............................................22
1.5 The Sylow Theorems..........................................31
1.6 Exercises........................................................35
2. Rings 41
2.1 Introduction to Rings..........................................42
2.2 Polynomial Rings..............................................48
2.3 The Group of Units of a Ring................................53
2.4 Ideals ..........................................................60
2.5 Quotient Rings and Ring Homomorphisms..................70
2.6 Localization....................................................78
2.7 Absolute Values and Completions............................82
2.8 Exercises........................................................93
3. Modules 101
3.1 Vector Spaces..................................................102
3.2 Modules........................................................109
3.3 Projective Modules............................................117
3.4 Tensor Products ..............................................122
3.5 Algebras........................................................128
3.6 Discriminants..................................................133
3.7 Exercises........................................................140
4. Simple Algebraic Extension Fields 143
4.1 Simple Algebraic Extensions..................................144
4.2 Some Galois Theory..........................................152
4.3 The Ring of Integers..........................................158
4.4 The Noetherian Property of the Ring of Integers..........169
4.5 Dedekind Domains............................................172
4.6 Unique Factorization of Ideals................................178
4.7 Extensions of Qp..............................................181
4.8 Exercises........................................................186
5. Finite Fields 191
5.1 Invented Roots................................................191
5.2 Finite Fields....................................................193
5.3 Linearly Recursive Sequences................................200
5.4 Exercises........................................................212
Bibliography 215
Index 217
|
| any_adam_object | 1 |
| author | Underwood, Robert G. |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:31:33Z |
| institution | BVB |
| isbn | 9789814730297 9789814730280 |
| language | English |
| lccn | 015040815 |
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| physical | x, 220 Seiten Illustrationen 24 cm |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Underwood, Robert G. (DE-588)1015211801 aut Fundamentals of modern algebra a global perspective Robert G. Underwood, Auburn University at Montgomery, USA. New Jersey World Scientific [2016] x, 220 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Algebra, Abstract Textbooks Algebra Textbooks Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029064538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Underwood, Robert G. Fundamentals of modern algebra a global perspective Algebra, Abstract Textbooks Algebra Textbooks Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | Fundamentals of modern algebra a global perspective |
| title_auth | Fundamentals of modern algebra a global perspective |
| title_exact_search | Fundamentals of modern algebra a global perspective |
| title_full | Fundamentals of modern algebra a global perspective Robert G. Underwood, Auburn University at Montgomery, USA. |
| title_fullStr | Fundamentals of modern algebra a global perspective Robert G. Underwood, Auburn University at Montgomery, USA. |
| title_full_unstemmed | Fundamentals of modern algebra a global perspective Robert G. Underwood, Auburn University at Montgomery, USA. |
| title_short | Fundamentals of modern algebra |
| title_sort | fundamentals of modern algebra a global perspective |
| title_sub | a global perspective |
| topic | Algebra, Abstract Textbooks Algebra Textbooks Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra, Abstract Textbooks Algebra Textbooks Algebra |
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