The structure of abstract algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Glenview, Ill.
Scott, Foresman
1970
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 423 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a The structure of abstract algebra |c Ralph B. Crouch ; David N. Beckman |
| 264 | 1 | |a Glenview, Ill. |b Scott, Foresman |c 1970 | |
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| 650 | 4 | |a Algèbre abstraite | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Sets, Relations, and Functions /
1.1 Set notation 2
1.2 Subsets of a set 6
1.3 The cartesian product of sets 11
1.4 Relations 15
1.5 Domain and range of a relation 21
1.6 Functions 25
1.7 Binary operations 31
1.8 Union and intersection of sets 35
1.9 Composition of functions 41
1.10 Equivalence relations 46
1.11 The integers modulo n 61
Chapter 2 Groups 57
2.1 Closure of binary operations 68
2.2 The associative property of binary operations 68
2.3 Semigroups and the existence of an identity 76
2.4 Semigroups and the existence of inverses 80
2.5 Properties of groups 84
2.6 Symmetric groups and permutation groups 95
2.7 Commutative groups 110
2.8 Subgroups of a group 116
2.9 Intersection and union of subgroups 124
2.10 Cyclic groups 130
2.11 Classification of cyclic groups 139
2.12 Products of groups 161
2.13 Construction of finite commutative groups 160
Chapter 3 Rings and Integral Domains 167
3.1 Rings 168
3.2 Commutative rings with identity 179
3.3 Elementary properties of a ring 186
3.4 Subrings 190
3.5 Ideals 196
3.6 Homomorphisms 199
3.7 Polynomial rings 206
3.8 Integral domains 216
Chapter 4 Fields 228
4.1 The properties of a field 224
4.2 The characteristic of a field 232
4.3 Subfields 239
4.4 Simple field extensions 24 6
Chapter 5 Vector Spaces 255
5.1 The definition and elementary properties
of a vector space 256
5.2 Subspaces of a vector space 266
5.3 Intersection of subspaces 279
5.4 Direct sum of subspaces 284
5.5 Linear independence and bases 290
5.6 Transformations of vector spaces 299
5.7 The vector space of linear transformations 313
5.8 The vector space of matrices 322
5.9 Subtraction and multiplication of matrices 328
Solutions for the odd numbered exercises 343
Index 411
|
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| author | Crouch, Ralph B. 1923-1975 Beckman, David N. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:49:00Z |
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| language | English |
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| publishDate | 1970 |
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| publisher | Scott, Foresman |
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| spelling | Crouch, Ralph B. 1923-1975 Verfasser (DE-588)1012209202 aut The structure of abstract algebra Ralph B. Crouch ; David N. Beckman Glenview, Ill. Scott, Foresman 1970 423 S. txt rdacontent n rdamedia nc rdacarrier Algebra Abstrata larpcal Algèbre abstraite Algèbre abstraite ram Algebra, Abstract Algebra (DE-588)4001156-2 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s DE-604 Algebra (DE-588)4001156-2 s Beckman, David N. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crouch, Ralph B. 1923-1975 Beckman, David N. The structure of abstract algebra Algebra Abstrata larpcal Algèbre abstraite Algèbre abstraite ram Algebra, Abstract Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4001166-5 |
| title | The structure of abstract algebra |
| title_auth | The structure of abstract algebra |
| title_exact_search | The structure of abstract algebra |
| title_full | The structure of abstract algebra Ralph B. Crouch ; David N. Beckman |
| title_fullStr | The structure of abstract algebra Ralph B. Crouch ; David N. Beckman |
| title_full_unstemmed | The structure of abstract algebra Ralph B. Crouch ; David N. Beckman |
| title_short | The structure of abstract algebra |
| title_sort | the structure of abstract algebra |
| topic | Algebra Abstrata larpcal Algèbre abstraite Algèbre abstraite ram Algebra, Abstract Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| topic_facet | Algebra Abstrata Algèbre abstraite Algebra, Abstract Algebra Algebraische Struktur |
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