SOLUTION MANUAL for First Course in Abstract Algebra A 8th Edition by John B. Fraleigh All Chapters 1-56, Complete

SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters 1-56, Complete V

, CONTENTS
0. SetsV andV Relations 1

I. GroupsV andV Subgroups

1. IntroductionV andV Examples 4
2. BinaryV Operations 7
3. IsomorphicV BinaryV Structures 9
4. Groups 13
5. Subgroups 17
6. CyclicV Groups 21
7. GeneratorsV andV CayleyV Digraphs 24

II. Permutations,V Cosets,V andV DirectV Products

8. GroupsV ofV Permutations 26
9. Orbits,VCycles,VandVtheVAlternatingVGroups 30
10. CosetsV andV theV TheoremV ofV Lagrange 34
11. DirectV ProductsV andV FinitelyV GeneratedV AbelianV Groups 37
12. PlaneV Isometries 42

III. HomomorphismsV andV FactorV Groups

13. Homomorphisms 44
14. FactorV Groups 49
15. Factor-GroupV ComputationsV andV SimpleV Groups 53
16. GroupV ActionVonV aVSet 58
17. ApplicationsVofVG-SetsVtoVCounting 61

IV. RingsV andV Fields

18. RingsV andV Fields 63
19. IntegralV Domains 68
20. Fermat’sV andV Euler’sV Theorems 72
21. TheV FieldV ofV QuotientsV ofV anV IntegralV Domain 74
22. RingsV ofV Polynomials 76
23. FactorizationVofVPolynomialsVoverVaVField 79
24. NoncommutativeV Examples 85
25. OrderedV RingsV andV Fields 87

V. IdealsV andV FactorV Rings

26. HomomorphismsV andV FactorV Rings 89
27. PrimeVandVMaximalVIdeals 94

,28. Grö bner VBasesVforVIdeals 99

, VI. ExtensionV Fields

29. IntroductionVtoV ExtensionV Fields 103
30. VectorV Spaces 107
31. AlgebraicV Extensions 111
32. GeometricV Constructions 115
33. FiniteV Fields 116

VII. AdvancedV GroupV Theory

34. IsomorphismVTheorems 117
35. SeriesVofVGroups 119
36. SylowV Theorems 122
37. ApplicationsV ofV theV SylowV Theory 124
38. FreeV AbelianV Groups 128
39. FreeVGroups 130
40. GroupV Presentations 133

VIII. GroupsV inV Topology

41. SimplicialV ComplexesV andV HomologyV Groups 136
42. ComputationsV ofV HomologyV Groups 138
43. MoreV HomologyV ComputationsV andV Applications 140
44. HomologicalV Algebra 144

IX. Factorization
45. UniqueV FactorizationV Domains 148
46. EuclideanV Domains 151
47. GaussianV IntegersV andV MultiplicativeV Norms 154

X. AutomorphismsV andV GaloisV Theory
48. AutomorphismsV ofV Fields 159
49. TheV IsomorphismV ExtensionV Theorem 164
50. SplittingV Fields 165
51. SeparableVExtensions 167
52. TotallyVInseparableVExtensions 171
53. GaloisV Theory 173
54. IllustrationsVofVGaloisVTheory 176
55. CyclotomicVExtensions 183
56. InsolvabilityV ofV theV Quintic 185

APPENDIXV MatrixV Algebra 187