Algebraic structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass [u.a.]
Addison-Wesley Publ. Co.
1968
|
| Edition: | 2. print. |
| Series: | Addison-Wesley series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 173 S. |
| ISBN: | 0201041731 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter I
The Integers
1. Terminology of sets 1
2. Basic properties 2
3. Greatest common divisor 5
4. Unique factorization 6
5. Equivalence relations and congruences 8
Chapter II
Groups
1. Groups and examples 12
2. Mappings 17
3. Homomorphisms 21
4. Cosets and normal subgroups 26
5. Permutation groups 32
6. Cyclic groups 39
Chapter III
Rings
1. Rings 43
2. Ideals 46
3. Homomorphisms 48
4. Quotient fields 54
Chapter IV
Polynomials
1. Euclidean algorithm 58
2. Greatest common divisor 63
3. Unique factorization 65
4. Partial fractions 70
5. Polynomials over the integers 76
6. Transcendental elements 79
7. Polynomials in several variables 84
vii
Viii CONTENTS
Chaptee V
Vector Spaces and Modules
1. Vector spaces and bases 86
2. Dimension of a vector space 92
3. Modules 94
Chapter VI
Field Theory
1. Algebraic extensions 102
2. Embeddings 105
3. Splitting fields 110
4. Fundamental theorem Ill
5. Quadratic and cubic extensions 113
6. Solvability by radicals 115
7. Infinite extensions 118
Chapter VII
The Real and Complex Numbers
1. Ordering of rings 120
2. Preliminaries 123
3. Construction of the real numbers 126
4. Decimal expansions 133
5. The complex numbers 136
Chapter VIII
Sets
1. More terminology 141
2. Zorn s lemma 144
3. Cardinal numbers 148
4. Well ordering 158
5. Proof of Zorn s lemma 160
Appendix
1. The natural numbers 164
2. The integers 168
3. Infinite sets 169
Index 171
|
| adam_txt |
Contents
Chapter I
The Integers
1. Terminology of sets 1
2. Basic properties 2
3. Greatest common divisor 5
4. Unique factorization 6
5. Equivalence relations and congruences 8
Chapter II
Groups
1. Groups and examples 12
2. Mappings 17
3. Homomorphisms 21
4. Cosets and normal subgroups 26
5. Permutation groups 32
6. Cyclic groups 39
Chapter III
Rings
1. Rings 43
2. Ideals 46
3. Homomorphisms 48
4. Quotient fields 54
Chapter IV
Polynomials
1. Euclidean algorithm 58
2. Greatest common divisor 63
3. Unique factorization 65
4. Partial fractions 70
5. Polynomials over the integers 76
6. Transcendental elements 79
7. Polynomials in several variables 84
vii
Viii CONTENTS
Chaptee V
Vector Spaces and Modules
1. Vector spaces and bases 86
2. Dimension of a vector space 92
3. Modules 94
Chapter VI
Field Theory
1. Algebraic extensions 102
2. Embeddings 105
3. Splitting fields 110
4. Fundamental theorem Ill
5. Quadratic and cubic extensions 113
6. Solvability by radicals 115
7. Infinite extensions 118
Chapter VII
The Real and Complex Numbers
1. Ordering of rings 120
2. Preliminaries 123
3. Construction of the real numbers 126
4. Decimal expansions 133
5. The complex numbers 136
Chapter VIII
Sets
1. More terminology 141
2. Zorn's lemma 144
3. Cardinal numbers 148
4. Well ordering 158
5. Proof of Zorn's lemma 160
Appendix
1. The natural numbers 164
2. The integers 168
3. Infinite sets 169
Index 171 |
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| author | Lang, Serge |
| author_facet | Lang, Serge |
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| discipline | Mathematik |
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| edition | 2. print. |
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| index_date | 2024-07-02T16:03:33Z |
| indexdate | 2024-07-09T20:46:29Z |
| institution | BVB |
| isbn | 0201041731 |
| language | English |
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| oclc_num | 312822760 |
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| physical | 173 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Addison-Wesley Publ. Co. |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics |
| spelling | Lang, Serge Verfasser aut Algebraic structures 2. print. Reading, Mass [u.a.] Addison-Wesley Publ. Co. 1968 173 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Algebra (DE-588)4001156-2 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Algebraische Struktur (DE-588)4001166-5 s DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015090605&sequence=000002&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 | Lang, Serge Algebraic structures Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4001166-5 (DE-588)4151278-9 |
| title | Algebraic structures |
| title_auth | Algebraic structures |
| title_exact_search | Algebraic structures |
| title_exact_search_txtP | Algebraic structures |
| title_full | Algebraic structures |
| title_fullStr | Algebraic structures |
| title_full_unstemmed | Algebraic structures |
| title_short | Algebraic structures |
| title_sort | algebraic structures |
| topic | Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| topic_facet | Algebra Algebraische Struktur Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015090605&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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