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A First Course in Abstract Algebra by John Fraleigh (2002, Hardcover, Revised edition)

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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. KEY TOPICS: 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; Gr bner 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 MARKET: For all readers interested in abstract algebra.

Product Identifiers

Publisher
Pearson Education
ISBN-10
0201763907
ISBN-13
9780201763904
eBay Product ID (ePID)
2041144

Product Key Features

Author
John B. Fraleigh, John Fraleigh
Publication Name
First Course in Abstract Algebra
Format
Hardcover
Language
English
Features
Revised
Publication Year
2002
Type
Textbook
Number of Pages
544 Pages, 590 Pages

Dimensions

Item Length
9.5in
Item Height
1in
Item Width
7.8in
Weight
35.8 Oz
Item Weight
35.5 Oz

Additional Product Features

Lc Classification Number
Qa162.F7 2002
Publication Date
2002-11-06
Edition Description
Revised, Revised Edition
Edition Number
7
Table of Content
(*) 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.
Copyright Date
2003
Topic
Algebra / Abstract, Algebra / General
Lccn
2002-019357
Dewey Decimal
512/.8, 512/.02
Intended Audience
College Audience
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics

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