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First Course in Abstract Algebra, A John Fraleigh

First Course in Abstract Algebra, A By John Fraleigh

First Course in Abstract Algebra, A by John Fraleigh

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Summary

Considered a classic by many, A First Course in Abstract Algebra 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.

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First Course in Abstract Algebra, A Summary

First Course in Abstract Algebra, A by John Fraleigh

This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory.

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. *Groebner 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.

Additional information

CIN0201763907VG
9780201763904
0201763907
First Course in Abstract Algebra, A by John Fraleigh
John Fraleigh
Used - Very Good
Hardback
Pearson Education (US)
20021216
544
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

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