Abstract algebra: an introduction with applications
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| Previous Title: | Robinson, Derek John Scott An introduction to abstract algebra |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2015
|
| Edition: | 2. ed. |
| Series: | De-Gruyter-Textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 337 S. Ill. |
| ISBN: | 9783110340860 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804174892963201024 |
|---|---|
| adam_text | Contents
Preface VII
1 Sets, relations and functions 1
1.1 Sets and subsets 1
1.2 Relations, equivalence relations, partial orders
1.3 Functions 9
1.4 Cardinality 13
2 The integers —— 17
2.1 Well-ordering and mathematical induction - —17
2.2 Division in the integers — 19
2.3 Congruences —— 24
3 Introduction to groups — 31
3.1 Permutations — 31
3.2 Semigroups, monoids and groups — 40
3.3 Groups and subgroups — 45
4 Quotient groups and homomorphisms 53
4.1 Cosets and Lagrange’s Theorem 53
4.2 Normal subgroups and quotient groups -61
4.3 Homomorphisms 68
5 Groups acting on sets —— 79
5.1 Group actions 79
5.2 Orbits and stabilizers 82
5.3 Applications to the structure of groups —- 86
5.4 Applications to combinatorics 93
6 Introduction to rings —100
6.1 Elementary properties of rings —100
6.2 Subrings and ideals — 104
6.3 Integral domains, division rings and fields —110
6.4 Finiteness conditions on ideals =— 117
7 Division in commutative rings֊—120
7.1 Euclidean domains —120
7.2 Principal ideal domains —123
7.3 Unique factorization in integral domains — -126
7.4 Roots of polynomials and splitting fields — • 132
X
Contents
8 Vector spaces-----139
8.1 Vector spaces and subspaces-----139
8.2 Linear independence, basis and dimension-----143
8.3 Linear mappings-----152
8.4 Eigenvalues and eigenvectors----160
9 Introduction to modules----173
9.1 Elements of module theory----173
9.2 Modules over principal ideal domains — 185
9.3 Applications to linear operators--197
10 The Structure of groups ~—- 206
10.1 The Jordan-Hôlder Theorem — 206
10.2 Solvable and nilpotent groups — 214
10.3 Theorems on finite solvable groups — 222
11 The Theory of fields ---227
11.1 Field extensions — 227
11.2 Constructions with ruler and compass —232
11.3 Finite fields--- 237
11.4 Latin squares and Steiner triple systems -—= 241
12 Galois Theory-----250
12.1 Normal and separable extensions------250
12.2 Automorphisms of field extensions----255
12.3 The Fundamental Theorem of Galois theory----263
12.4 Solvability of equations by radicals-269
13 Tensor products —- 276
13.1 Definition of the tensor product--276
13.2 Properties of tensor products. —— 281
13.3 Extending the ring of operators. — 288
14 Further topics — 293
14.1 Zorn’s Lemma with applications * 293
14.2 Roots of polynomials and discriminants 299
14.3 Presentations of groups --302
14.4 Introduction to error correcting codes —— 313
Bibliography —- 326
List of symbols — 327
Index — 329
|
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| author | Robinson, Derek John Scott 1938- |
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| ctrlnum | (OCoLC)893439423 (DE-599)BVBBV042695992 |
| dewey-full | 512/.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.02 |
| dewey-search | 512/.02 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Robinson, Derek John Scott 1938- Verfasser (DE-588)1017969213 aut Abstract algebra an introduction with applications Derek J. S. Robinson 2. ed. Berlin [u.a.] de Gruyter 2015 X, 337 S. Ill. txt rdacontent n rdamedia nc rdacarrier De-Gruyter-Textbook Álgebra abstrata larpcal Algebra, Abstract Algebra (DE-588)4001156-2 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Universelle Algebra (DE-588)4061777-4 s DE-604 Algebra (DE-588)4001156-2 s Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038560-1 Erscheint auch als Online-Ausgabe, PDF 978-3-11-034087-7 Früher u.d.T. Robinson, Derek John Scott An introduction to abstract algebra Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028127577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robinson, Derek John Scott 1938- Abstract algebra an introduction with applications Álgebra abstrata larpcal Algebra, Abstract Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4061777-4 (DE-588)4123623-3 |
| title | Abstract algebra an introduction with applications |
| title_auth | Abstract algebra an introduction with applications |
| title_exact_search | Abstract algebra an introduction with applications |
| title_full | Abstract algebra an introduction with applications Derek J. S. Robinson |
| title_fullStr | Abstract algebra an introduction with applications Derek J. S. Robinson |
| title_full_unstemmed | Abstract algebra an introduction with applications Derek J. S. Robinson |
| title_old | Robinson, Derek John Scott An introduction to abstract algebra |
| title_short | Abstract algebra |
| title_sort | abstract algebra an introduction with applications |
| title_sub | an introduction with applications |
| topic | Álgebra abstrata larpcal Algebra, Abstract Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Álgebra abstrata Algebra, Abstract Algebra Universelle Algebra Lehrbuch |
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