An edition of Abstract algebra (1991)

Abstract algebra

3rd ed.

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Cover of: Abstract algebra by David S. Dummit, Richard M. Foote.
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Last edited by ImportBot
December 19, 2023 | History
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An edition of Abstract algebra (1991)

Abstract algebra

3rd ed.

by

  • ★★★ 3.00 ·
  • 1 Rating
  • 27 Want to read
  • 3 Currently reading
  • 3 Have read

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Publish Date
Publisher
Wiley
Language
English
Pages
932

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Previews available in: English

Subjects
Abstract Algebra, Algebra, Abstract, Algebra, abstract, Algèbre abstraite, Algebra, Algebraische Struktur, Álgebra abstrata

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Edition Availability
Cover of: Abstract Algebra
Abstract Algebra
2004, Wiley
in English - Third edition. Student edition.
Libraries near you: WorldCat
Cover of: Abstract algebra
Abstract algebra
2004, Wiley
Hardcover in English - 3rd ed.
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Libraries near you: WorldCat
Cover of: Abstract algebra
Abstract algebra
1999, Prentice Hall
in English - 2nd ed.
Libraries near you: WorldCat
Cover of: Abstract algebra
Abstract algebra
1991, Prentice Hall
in English
Libraries near you: WorldCat

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Book Details

Published in

Hoboken, NJ

Table of Contents

Preface Page xi
Preliminaries Page 1 0.1. Basics Page 1
0.2. Properties of the Integers
0.3. Z/nZ: The Integers Modulo n Page 8 Part I. Group Theory Page 13 1. Introduction to Groups Page 16 1.1. Basic Axioms and Examples Page 16 1.2. Dihedral Groups Page 23 1.3. Symmetric Groups Page 29 1.4. Matrix Groups Page 34 1.5. The Quaternion Group Page 36 1.6. Homomorphisms and Isomorphisms Page 36 1.7. Group Actions Page 41 2. Subgroups Page 46 2.1. Definitions and Examples Page 46 2.2. Centralizers and Normalizers, Stabilizers and Kernels Page 49 2.3. Cyclic Groups and Cyclic Subgroups Page 54 2.4. Subgroups Generated by Subsets of a Group Page 61 2.5. The Lattice of Subgroups of a Group Page 66 3. Quotient Groups and Homomorphisms Page 73 3.1. Definitions and Examples Page 73 3.2. More on Cosets and Lagrange's Theorem Page 89 3.3. The Isomorphism Theorems Page 97 3.4. Composition Series and the Holder Program Page 101 3.5. Transpositions and the Alternating Group Page 106 4. Group Actions Page 112 4.1. Group Actions and Permutation Representations Page 112 4.2. Groups Acting on Themselves by Left Multiplication-Cayley's Theorem Page 118 4.3. Groups Acting on Themselves by Conjugation-The Class Equation Page 122 4.4. Automorphism Page 133 4.5. The Sylow Theorems Page 139 4.6. The Simplicity of An Page 149 5. Direct and Semidirect Products and Abelian Groups Page 152 5.1. Direct Products Page 142 5.2. The Fundamental Theorem of Finitely Generated Ableian Groups Page 158 5.3. Table of Groups of Small Order Page 167 5.4. Recognizing Direct Products Page 169 5.5. Semidirect Products Page 175 6. Further Topics in Group Theory Page 188 6.1. p-groups, Nilpotent Groups, and Solvable Groups Page 188 6.2. Applications in Groups of Medium Order Page 201 6.3. A Word on Free Groups Page 215 Part II. Ring Theory Page 222 7. Introduction to Rings Page 223 7.1. Basic Definitions and Exmaples Page 223 7.2. Examples: Polynomial Rings, Matri Rings, and Group Rings Page 233 7.3. Ring Homomorphisms and Quotinet Rings Page 239 7.4. Properties of Ideals Page 251 7.5. Rings of fractions Page 260 7.6. The Chinese Remainder Theorem Page 265 8. Euclidean Domains, Principla Ideal Domains and Unique Factorization Domains Page 270 8.1. Euclidean Domains Page 270 8.2. Principal Ideal Domains (P.I.D.s) Page 279 8.3. Unique Factorization Domains (U.F.D.s) Page 283 9. Polynomial Rings Page 295 9.1. Definitions and Basic Properties Page 295 9.2. Polynomial Rings over Fields I Page 299 9.3. Polynomial Rings that are Unique Factorization Domains Page 303 9.4. Irreducibility Criteria Page 307 9.5. Polynomial rings over Fields II Page 313 9.6. Polynomials in Several Variables over a Field and Grobner Bases Page 315 Part III. Modules and Vector Spaces Page 336 10. Introduction to Module Theory Page 337 10.1. Basic Definitions and Examples Page 337 10.2. Quotient Modules and Module Homomorphisms Page 345 10.3. Generation of Modules, Direct Sums, and Free Modules Page 351 10.4. Tensor Product of Modules Page 359 10.5. Exact Sequences - Projective, Injective, and Flat Modules Page 378 11. vector Spaces Page 408 11.1. Definitions and Basic Theory Page 408 11.2. The Matrix of a Linear Transformation Page 415 11.3. Dual Vector Spaces Page 431 11.4. Determinants Page 435 11.5. Tensor Algebras, Symmetric and Exterior Algebras Page 441 12. Modules over Principal Ideal Domains Page 456 12.1. The Basic Theory Page 458 12.2. The Rational Canonical From Page 472 12.3. The Jordan Canonical From Page 491 13. Field Theory Page 510 13.1. Basic Theory of field Extensions Page 510 13.2. Algebraic extensions Page 520 13.3. Classical Straightedge and Compass Constructions Page 531 13.4. Splitting Fields and Algebraic Closures Page 536 13.5. Separable and Inseparable Extensions Page 545 13.6. Cyclotomic Polynomials and Extensions Page 552 14. Galios Theory Page 558 14.1. Basic Definitions Page 558 14.2. The Fundamental Theorem of Galios Theory Page 567 14.3. Finite Fields Page 585 14.4. Composite Extensions and Simple Extensions Page 591 14.5. Cyclotomic Extensions and Albelian Extensions over Q Page 596 14.6. Galois Groups of Polynomials Page 606 14.7. Solvable and Radical Extensions: Insolvability of the Quintic Page 625 14.8. Computation of the Galois Groups over Q Page 640 14.9. Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups Page 645 Part V [sic]. An Introduction to Comutative Rings, Algebraic Geometry, and Homological Algebra Page 655 15. Commutative Rings and Algebraic Geometry Page 656 15.1. Noetherian Rings and Affine Algebraic Sets Page 656 15.2. Radicals and Affine Varieties Page 673 15.3. Integral Extensions and Hilbert's Nullstellensatz Page 691 15.4. Localization Page 706 15.5. The Prime Spectrum of a Ring Page 731 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains Page 750 16.1. Artinian Rings Page 750 16.2. Discrete Valuation Rings Page 755 16.3. Dedekind Domains Page 764 17. Introduction to Homological Algebra and Group Cohomology Page 776 17.1. Introduction to Homological Algebra - Ext and Tor Page 777 17.2. The Cohomology of Groups Page 798 17.3. Crossed Homomorphisms and H1(G, A) Page 814 17.4. Group Extensions, Factor Sets and H2(G, A) Page 824 Part VI. Introduction to the Representation Theory of Finite Groups Page 839 18. Representation Theory and Character Theory Page 840 18.1. Linear Actions and Modules over Group Rings Page 840 18.2. Wedderburn's Theorem and Some Consequences Page 854 18.3. Character Theory and the Orthogonality Relations Page 864 19. Examples and Applications of Character Theory Page 880 19.1. Characters of Groups of Small Order Page 880 19.2. Theorems of Burnside and Hall Page 886 19.3. Introduction to the Theory of Induced Characters Page 892 Appendix I. Cartesian Products and Zorn's Lemma Page 905 Appendix II. Category Theory Page 911 Index Page 919

Edition Notes

Includes index.

Classifications

Dewey Decimal Class
512/.02
Library of Congress
QA162 .D85 2004, QA162.D85 2004

The Physical Object

Format
Hardcover
Pagination
xii, 932 p.
Number of pages
932

ID Numbers

Open Library
OL3689578M
Internet Archive
abstractalgebrar00dumm
ISBN 10
0471433349
LCCN
2003057652
OCLC/WorldCat
52559229
Library Thing
75767
Goodreads
264543

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December 19, 2023 Edited by ImportBot import existing book
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