Problems in abstract algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2017]
|
| Schriftenreihe: | Student mathematical library
82 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 277 Seiten |
| ISBN: | 9781470435837 |
Internformat
MARC
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| 100 | 1 | |a Wadsworth, Adrian R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Problems in abstract algebra |c A.R. Wadsworth |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2017] | |
| 264 | 4 | |c © 2017 | |
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| 490 | 1 | |a Student mathematical library |v volume 82 | |
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| 650 | 7 | |a Group theory and generalizations / Instructional exposition (textbooks, tutorial papers, etc.) |2 msc | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
•»
Vll
Introduction..........................
§0.1. Notation......................
§0.2. Zorn’s Lemma..................
Chapter 1. Integers and Integers mod n
Chapter 2. Groups.........................................
§2.1. Groups, subgroups, and cosets.....................
§2.2. Group homomorphisms and factor groups . . . .
§2.3. Group actions.....................................
§2.4. Symmetric and alternating groups .................
§2.5. p-groups..........................................
§2.6. Sylow subgroups...................................
§2.7. Semidirect products of groups ....................
§2.8. Free groups and groups by generators and relations
§2.9. Nilpotent, solvable, and simple groups ...........
§2.10. Finite abelian groups . . . .....................
Chapter 3. Rings..........................................
§3.1. Rings, subrings, and ideals.......................
1
3
5
7
13
13
25
32
36
41
43
44
53
58
66
73
73
3.2. Factor rings and ring homomorphisms ................ 89
3.3. Polynomial rings and evaluation maps ............... 97
3.4. Integral domains, quotient fields ................. 100
3.5. Maximal ideals and prime ideals.................... 103
3.6. Divisibility and principal ideal domains........... 107
3.7. Unique factorization domains ...................... 115
Chapter
§4.1.
§4.2.
§4.3.
§4.4.
§4.5.
§4.6.
§4.7.
§4.8.
§4.9.
§4.10.
§4.11.
§4.12.
4. Linear Algebra and Canonical Forms of Linear
Transformations ..................................
Vector spaces and linear dependence.............
Linear transformations and matrices.............
Dual space......................................
Determinants ...................................
Eigenvalues and eigenvectors, triangulation and
diagonalization ................................
Minimal polynomials of a linear transformation
and primary decomposition ................... . .
T-cyclic subspaces and T-annihilators ..........
Projection maps.................................
Cyclic decomposition and rational and Jordan
canonical forms ................................
The exponential of a matrix ....................
Symmetric and orthogonal matrices over №.....
Group theory problems using linear algebra . . .
Chapter 5. Fields and Galois Theory...........................
§5.1. Algebraic elements and algebraic field extensions .
§5.2. Constructibility by compass and straightedge . . .
§5.3. Transcendental extensions ............................
§5.4. Criteria for irreducibility of polynomials ...........
§5.5. Splitting fields, normal field extensions, and Galois
groups ....................................................
§5.6. Separability and repeated roots ......................
125
125
132
139
142
150
155
161
164
167
177
180
187
191
192
199
202
205
208
216
§5.7. Finite fields ...................................... 223
§5.8. Galois field extensions............................. 226
§5.9. Cyclotomic polynomials and cyclotomic extensions 234
§5.10. Radical extensions, norms, and traces .............. 244
§5.11. Solvability by radicals ............................ 253
Suggestions for Further Reading .............................. 257
Bibliography.................................................. 259
Index of Notation ............................................ 261
Subject and Terminology Index................................. 267
|
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| isbn | 9781470435837 |
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| spelling | Wadsworth, Adrian R. Verfasser aut Problems in abstract algebra A.R. Wadsworth Providence, Rhode Island American Mathematical Society [2017] © 2017 viii, 277 Seiten txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 82 Includes bibliographical references and index Algebra, Abstract / Textbooks Algebra, Abstract fast General / General and miscellaneous specific topics / Problem books msc Field theory and polynomials / Instructional exposition (textbooks, tutorial papers, etc.) msc Commutative algebra / Instructional exposition (textbooks, tutorial papers, etc.) msc Linear and multilinear algebra; matrix theory / Instructional exposition (textbooks, tutorial papers, etc.) msc Group theory and generalizations / Instructional exposition (textbooks, tutorial papers, etc.) msc Problem (DE-588)4175771-3 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 Problem (DE-588)4175771-3 s DE-604 Student mathematical library 82 (DE-604)BV013184751 82 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=029667655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wadsworth, Adrian R. Problems in abstract algebra Student mathematical library Includes bibliographical references and index Algebra, Abstract / Textbooks Algebra, Abstract fast General / General and miscellaneous specific topics / Problem books msc Field theory and polynomials / Instructional exposition (textbooks, tutorial papers, etc.) msc Commutative algebra / Instructional exposition (textbooks, tutorial papers, etc.) msc Linear and multilinear algebra; matrix theory / Instructional exposition (textbooks, tutorial papers, etc.) msc Group theory and generalizations / Instructional exposition (textbooks, tutorial papers, etc.) msc Problem (DE-588)4175771-3 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4175771-3 (DE-588)4061777-4 (DE-588)4123623-3 |
| title | Problems in abstract algebra |
| title_auth | Problems in abstract algebra |
| title_exact_search | Problems in abstract algebra |
| title_full | Problems in abstract algebra A.R. Wadsworth |
| title_fullStr | Problems in abstract algebra A.R. Wadsworth |
| title_full_unstemmed | Problems in abstract algebra A.R. Wadsworth |
| title_short | Problems in abstract algebra |
| title_sort | problems in abstract algebra |
| topic | Algebra, Abstract / Textbooks Algebra, Abstract fast General / General and miscellaneous specific topics / Problem books msc Field theory and polynomials / Instructional exposition (textbooks, tutorial papers, etc.) msc Commutative algebra / Instructional exposition (textbooks, tutorial papers, etc.) msc Linear and multilinear algebra; matrix theory / Instructional exposition (textbooks, tutorial papers, etc.) msc Group theory and generalizations / Instructional exposition (textbooks, tutorial papers, etc.) msc Problem (DE-588)4175771-3 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Algebra, Abstract / Textbooks Algebra, Abstract General / General and miscellaneous specific topics / Problem books Field theory and polynomials / Instructional exposition (textbooks, tutorial papers, etc.) Commutative algebra / Instructional exposition (textbooks, tutorial papers, etc.) Linear and multilinear algebra; matrix theory / Instructional exposition (textbooks, tutorial papers, etc.) Group theory and generalizations / Instructional exposition (textbooks, tutorial papers, etc.) Problem Universelle Algebra Lehrbuch |
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