Abstract algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2004
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes index. |
| Beschreibung: | XII, 932 S. Ill. |
| ISBN: | 0471433349 |
Internformat
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| 250 | |a 3. ed. | ||
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| 300 | |a XII, 932 S. |b Ill. | ||
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| 650 | 4 | |a Algèbre abstraite | |
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| 650 | 7 | |a Álgebra abstrata |2 larpcal | |
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| 700 | 1 | |a Foote, Richard M. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804130160186753024 |
|---|---|
| adam_text | Titel: Abstract algebra
Autor: Dummit, David S
Jahr: 2004
Contents
Preface xi
Preliminaries 1
0.1 Basics 1
0.2 Properties of the Integers 4
0.3 Z/nZ: The Integers Modulo n
8
Part I - GROUP THEORY 13
Chapter 1 Introduction to Groups 16
1.1 Basic Axioms and Examples 16
1.2 Dihedral Groups 23
1.3 Symmetric Groups 29
1.4 Matrix Groups 34
1.5 The Quaternion Group 36
1.6 Homomorphisms and Isomorphisms
1.7 Group Actions 41
36
Chapter 2 Subgroups 46
2.1 Definition and Examples 46
2.2 Centralizers and Normalizers, Stabilizers and Kernels
49
2.3 Cyclic Groups and Cyclic Subgroups 54
2.4 Subgroups Generated by Subsets of a Group 61
2.5 The Lattice of Subgroups of a Group 66
Contents
Chapter 3 Quotient Groups and Homomorphisms 73
3.1 Definitions and Examples 73
3.2 More on Cosets and Lagrange s Theorem 89
3.3 The Isomorphism Theorems 97
3.4 Composition Series and the Holder Program 101
3.5 Transpositions and the Alternating Group 106
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
Group Actions 112
Group Actions and Permutation Representations 112
Groups Acting on Themselves by Left Multiplication?Cayley s
Theorem 118
Groups Acting on Themselves by Conjugation?The Class
Equation 122
Automorphisms 133
The Sylow Theorems 139
The Simplicity of An 149
Chapter 5 Direct and Semidirect Products and Abelian Groups 152
5.1 Direct Products 152
5.2 The Fundamental Theorem of Finitely Generated Abelian
Groups 158
5.3 Table of Groups of Small Order 167
5.4 Recognizing Direct Products 169
5.5 Semidirect Products 175
Chapter 6 Further Topics in Group Theory 188
6.1 p-groups, Nilpotent Groups, and Solvable Groups 188
6.2 Applications in Groups of Medium Order 201
6.3 A Word on Free Groups 215
Part II - RING THEORY 222
Chapter 7
7.1
7.2
7.3
7.4
7.5
7.6
Introduction to Rings 223
Basic Definitions and Examples 223
Examples: Polynomial Rings, Matrix Rings, and Group
Rings 233
Ring Homomorphisms and Quotient Rings 239
Properties of ideals 251
Rings of Fractions 260
The Chinese Remainder Theorem 265
VI
Contents
Chapter 8 Euclidean Domains, Principal Ideal Domains and
Unique Factorization Domains 270
8.1 Euclidean Domains 270
8.2 Principal Ideal Domains (P.I.D.s) 279
8.3 Unique Factorization Domains (U.F.D.s) 283
Chapter 9 Polynomial Rings 295
9.1 Definitions and Basic Properties 295
9.2 Polynomial Rings over Fields I 299
9.3 Polynomial Rings that are Unique Factorization Domains
303
9.4 Irreducibility Criteria 307
9.5 Polynomial Rings over Fields II 313
9.6 Polynomials in Several Variables over a Field and Grobner
Bases 315
Part III - MODULES AND VECTOR SPACES 336
Chapter 10 Introduction to Module Theory 337
10.1 Basic Definitions and Examples 337
10.2 Quotient Modules and Module Homomorphisms 345
10.3 Generation of Modules, Direct Sums, and Free Modules
351
10.4 Tensor Products of Modules 359
10.5 Exact Sequences?Projective, Injective, and Flat Modules
378
Chapter 11 Vector Spaces 408
11.1 Definitions and Basic Theory 408
11.2 The Matrix of a Linear Transformation 415
11.3 Dual Vector Spaces 431
11.4 Determinants 435
11.5 Tensor Algebras, Symmetric and Exterior Algebras 441
Chapter 12 Modules over Principal Ideal Domains 456
The Basic Theory 458
12.1
12.2
12.3
The Rational Canonical Form 472
The Jordan Canonical Form 491
Contents
VII
Part IV - FIELD THEORY AND GALOIS THEORY 509
Chapter 13 Field Theory 510
13.1 Basic Theory of Field Extensions 510
13.2 Algebraic Extensions 520
13.3 Classical Straightedge and Compass Constructions 531
13.4 Splitting Fields and Algebraic Closures 536
13.5 Separable and Inseparable Extensions 545
13.6 Cyclotomic Polynomials and Extensions 552
Chapter 14 Galois Theory 558
14.1 Basic Definitions 558
14.2 The Fundamental Theorem of Galois Theory 567
14.3 Finite Fields 585
14.4 Composite Extensions and Simple Extensions 591
14.5 Cyclotomic Extensions and Abelian Extensions over Q
596
14.6 Galois Groups of Polynomials 606
14.7 Solvableand Radical Extensions: InsolvabilityoftheQuintic
625
14.8 Computation of Galois Groups over Q 640
14.9 Transcendental Extensions, Inseparable Extensions, Infinite
Galois Groups 645
Part V - AN INTRODUCTION TO COMMUTATIVE RINGS,
ALGEBRAIC GEOMETRY, AND
HOMOLOGICAL ALGEBRA 655
Commutative Rings and Algebraic Geometry 656
Noetherian Rings and Affine Algebraic Sets 656
Radicals and Affine Varieties 673
Integral Extensions and Hilbert s Nullstellensatz 691
Localization 706
The Prime Spectrum of a Ring 731
Artinian Rings, Discrete Valuation Rings, and
Dedekind Domains 750
16.1 Artinian Rings 750
16.2 Discrete Valuation Rings 755
16.3 Dedekind Domains 764
VMI Contents
Chapter 15
15.1
15.2
15.3
15.4
15.5
Chapter 16
Chapter 17 Introduction to Homological Algebra and
Group Cohomology 776
17.1 Introduction to Homological Algebra?Ext and Tor
17.2 The Cohomology of Groups 798
17.3 Crossed Homomorphisms and H1(G, A) 814
17.4 Group Extensions, Factor Sets and H2(G, A) 824
777
Part VI - INTRODUCTION TO THE REPRESENTATION
THEORY OF FINITE GROUPS 839
Chapter 18 Representation Theory and Character Theory 840
18.1 Linear Actions and Modules over Group Rings 840
18.2 Wedderburn s Theorem and Some Consequences 854
18.3 Character Theory and the Orthogonality Relations 864
Chapter 19 Examples and Applications of Character Theory 880
19.1 Characters of Groups of Small Order 880
19.2 Theorems of Burnside and Hall 886
19.3 Introduction to the Theory of Induced Characters 892
Appendix I: Cartesian Products and Zorn s Lemma 905
Appendix II: Category Theory 911
Index 919
Contents
IX
|
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| discipline | Mathematik |
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| spelling | Dummit, David S. Verfasser aut Abstract algebra David S. Dummit ; Richard M. Foote 3. ed. Hoboken, NJ Wiley 2004 XII, 932 S. Ill. txt rdacontent n rdamedia nc rdacarrier Includes index. Algèbre abstraite Algèbre abstraite rasuqam Álgebra abstrata larpcal Algebra, Abstract Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s Algebra (DE-588)4001156-2 s DE-604 Universelle Algebra (DE-588)4061777-4 s 1\p DE-604 Foote, Richard M. Sonstige oth http://www.loc.gov/catdir/description/wiley039/2003057652.html Publisher description http://www.loc.gov/catdir/toc/wiley032/2003057652.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441276&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 |
| spellingShingle | Dummit, David S. Abstract algebra Algèbre abstraite Algèbre abstraite rasuqam Álgebra abstrata larpcal Algebra, Abstract Algebraische Struktur (DE-588)4001166-5 gnd Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4001166-5 (DE-588)4001156-2 (DE-588)4061777-4 |
| title | Abstract algebra |
| title_auth | Abstract algebra |
| title_exact_search | Abstract algebra |
| title_full | Abstract algebra David S. Dummit ; Richard M. Foote |
| title_fullStr | Abstract algebra David S. Dummit ; Richard M. Foote |
| title_full_unstemmed | Abstract algebra David S. Dummit ; Richard M. Foote |
| title_short | Abstract algebra |
| title_sort | abstract algebra |
| topic | Algèbre abstraite Algèbre abstraite rasuqam Álgebra abstrata larpcal Algebra, Abstract Algebraische Struktur (DE-588)4001166-5 gnd Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Algèbre abstraite Álgebra abstrata Algebra, Abstract Algebraische Struktur Algebra Universelle Algebra |
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