Solution Manual for First Course in Abstract Algebra A, 8th Edition by John B. Fraleigh, Verified Chapters 1 - 56, Complete Newest Version

SOLUTION MANUAL First Course in Abstract
Algebra A 8th Edition by John B. Fraleigh
All Chapters Full Complete

, CONTENTS

1. Sets and Relations 1
NJ NJ




I. Groups and Subgroups
N J N J




2. Introduction and Examples 4 NJ NJ




3. Binary Operations 7
N J




4. Isomorphic Binary Structures 9 N J N J




5. Groups 13
6. Subgroups 17
7. Cyclic Groups 21
NJN J




8. Generators and Cayley Digraphs 24 NJ NJ NJ




II. Permutations, Cosets, and Direct Products NJ NJ NJ NJ




9. Groups of Permutations 26
NJ NJ




10. Orbits, Cycles, and the Alternating Groups
NJ NJ NJ NJ NJ




30
11. Cosets and the Theorem of Lagrange 34
NJ NJ NJ NJ NJ




12. Direct Products and Finitely Generated Abelian Groups 37
N J N J N J N J N J N J




13. Plane Isometries 42
N J




III. Homomorphisms and Factor Groups N J N J N J




14. Homomorphisms 44
15. Factor Groups 49
NJ




16. Factor-Group Computations and Simple Groups N J N J N J N J 53
17. Group Action on a Set 58
NJ NJ NJ NJ




18. Applications of G-Sets to Counting 61 NJ NJ NJ NJ

, IV. Rings and Fields N J N J




19. Rings and Fields 63
NJ NJ




20. Integral Domains 68
NJ




21. Fermat’s and Euler’s Theorems 72
N J N J N J




22. The Field of Quotients of an Integral Domain
N J NJ N J N J N J NJ N J 74
23. Rings of Polynomials 76
N J N J




24. Factorization of Polynomials over a Field 79
NJ NJ NJ NJ NJ




25. Noncommutative Examples 85 NJ




26. Ordered Rings and Fields 87
NJ N J N J




V. Ideals and Factor Rings N J N J N J




27. Homomorphisms and Factor Rings 89 NJ NJ NJ




28. Prime and Maximal Ideals 94
NJ NJ NJ




29. Gröbner Bases for Ideals 99
NJ NJ NJ

, VI. Extension Fields N J




30. Introduction to Extension Fields 103 NJ NJ NJ




31. Vector Spaces 107
N J




32. Algebraic Extensions 111 N J




33. Geometric Constructions 115 NJ




34. Finite Fields 116
NJ




VII. Advanced Group Theory NJ NJ




35. Isomorphism Theorems 117 N
J




36. Series of Groups 119
NJ NJ




37. Sylow Theorems 122
NJ




38. Applications of the Sylow Theory 124 N J N J N J N J




39. Free Abelian Groups 128
N J N J




40. Free Groups 130
NJ




41. Group Presentations 133
NJ




VIII. Groups in Topology N J N J




42. Simplicial Complexes and Homology Groups
NJ N J NJ NJ 136
43. Computations of Homology Groups 138 NJ NJ NJ




44. More Homology Computations and Applications
NJ NJ NJ NJ 140
45. Homological Algebra 144 NJ




IX. Factorization

46. Unique Factorization Domains 148
NJ N J




47. Euclidean Domains 151 N J




48. Gaussian Integers and Multiplicative Norms 154
NJ N J N J N J




X. Automorphisms and Galois Theory N J N J N J