A First Course in Abstract Algebra / Edition 7

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Overview

Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gröbner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra

For all readers interested in abstract algebra.

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Editorial Reviews

Booknews
An introductory textbook for the first course in abstract algebra. This edition (4th ed., 1989) includes applications to coding, finite- state machines (automata), graph theory, and isometry groups of the plane with the attendant Escher art works. A number of new examples and exercises are drawn from linear algebra, which many students have studied. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780201763904
  • Publisher: Pearson
  • Publication date: 11/6/2002
  • Edition description: REV
  • Edition number: 7
  • Pages: 536
  • Sales rank: 153,714
  • Product dimensions: 7.50 (w) x 9.30 (h) x 1.00 (d)

Table of Contents

(*) Not required for the remainder of the text. (**) This section is required only for Chapters 17 and 36.).

0. Sets and Relations.

I. GROUPS AND SUBGROUPS.

1. Introduction and Examples.

2. Binary Operations.

3. Isomorphic Binary Structures.

4. Groups.

5. Subgroups.

6. Cyclic Groups.

7. Generators and Cayley Digraphs.

II. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS.

8. Groups of Permutations.

9. Orbits, Cycles, and the Alternating Groups.

10. Cosets and the Theorem of Lagrange.

11. Direct Products and Finitely Generated Abelian Groups.

12. *Plane Isometries.

III. HOMOMORPHISMS AND FACTOR GROUPS.

13. Homomorphisms.

14. Factor Groups.

15. Factor-Group Computations and Simple Groups.

16. **Group Action on a Set.

17. *Applications of G-Sets to Counting.

IV. RINGS AND FIELDS.

18. Rings and Fields.

19. Integral Domains.

20. Fermat's and Euler's Theorems.

21. The Field of Quotients of an Integral Domain.

22. Rings of Polynomials.

23. Factorization of Polynomials over a Field.

24. *Noncommutative Examples.

25. *Ordered Rings and Fields.

V. IDEALS AND FACTOR RINGS.

26. Homomorphisms and Factor Rings.

27. Prime and Maximal Ideas.

28. *Gröbner Bases for Ideals.

VI. EXTENSION FIELDS.

29. Introduction to Extension Fields.

30. Vector Spaces.

31. Algebraic Extensions.

32. *Geometric Constructions.

33. Finite Fields.

VII. ADVANCED GROUP THEORY.

34. Isomorphism Theorems.

35. Series of Groups.

36. Sylow Theorems.

37. Applications of the Sylow Theory.

38. Free Abelian Groups.

39. Free Groups.

40. Group Presentations.

VIII. *GROUPS IN TOPOLOGY.

41. Simplicial Complexes and Homology Groups.

42. Computations of Homology Groups.

43. More Homology Computations and Applications.

44. Homological Algebra.

IX. Factorization.

45. Unique Factorization Domains.

46. Euclidean Domains.

47. Gaussian Integers and Multiplicative Norms.

X. AUTOMORPHISMS AND GALOIS THEORY.

48. Automorphisms of Fields.

49. The Isomorphism Extension Theorem.

50. Splitting Fields.

51. Separable Extensions.

52. *Totally Inseparable Extensions.

53. Galois Theory.

54. Illustrations of Galois Theory.

55. Cyclotomic Extensions.

56. Insolvability of the Quintic.

Appendix: Matrix Algebra.

Notations.

Answers to odd-numbered exercises not asking for definitions or proofs.

Index.

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Customer Reviews

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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted January 11, 2005

    The Best!

    This is the best text covering the subject matter. Take it from someone who knows. If it's too hard to read on your own, seek help. That's the way things work.

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  • Anonymous

    Posted April 22, 2004

    Half a book

    NOT for self study and not recommended for a classroom text. Some sections are well written, but too many answers to problems/proofs are not given. You are blind as you go. Frahleigh also puts problems ahead of sections. This is the 7th edition and still the author, while obviously knowledgble hasn't a clue what students need to be able to learn. ANYBODY CAN WRITE A BOOK WITHOUT ANSWERS. WE NEED ANSWERS AS WE GO...FEEDBACK SO WE STAY ON COURSE. Like many other text books this one appears to have been written not for students but for the author's professional peer group. Save your money. He won't help you!

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  • Anonymous

    Posted November 16, 2008

    No text was provided for this review.

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