A First Course in Abstract Algebra, 7th Edition Fraleigh

A First Course in Abstract Algebra, 7th Edition – Ebook Instant Download/Delivery ISBN(s): 9780201763904,0201763907

Product details:

• ISBN-10 ‏ : ‎ 0201763907
• ISBN-13 ‏ : ‎ 978-0201763904
• Author: John Fraleigh 

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.

Table of contents:

• 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. Grouml;bner 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

People also search: