SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. SetsF andF Relations 1
I. GroupsF andF Subgroups
2. IntroductionF andF Examples 4
3. BinaryF Operations 7
4. IsomorphicF BinaryF Structures 9
5. Groups 13
6. Subgroups 17
7. CyclicFF Groups 21
8. GeneratorsF andF CayleyF Digraphs 24
II. Permutations,FCosets,FandFDirectFProducts
9. GroupsF ofFPermutations 26
10. Orbits,FCycles,FandFtheFAlternatingFGroups
30
11. CosetsF andFtheF TheoremFofF Lagrange 34
12. DirectF ProductsF andF FinitelyF GeneratedF AbelianF Groups 37
13. PlaneF Isometries 42
III. HomomorphismsF andF FactorF Groups
14. Homomorphisms 44
15. FactorF Groups 49
16. Factor-GroupF ComputationsF andF SimpleF Groups 53
17. GroupFActionFonFaFSet 58
18. ApplicationsFofFG-SetsFtoFCounting 61
IV. RingsF andF Fields
19. RingsFandFFields 63
20. IntegralF Domains 68
21. Fermat’sF andF Euler’sF Theorems 72
22. TheF FieldF ofF QuotientsF ofF anF IntegralF Domain 74
23. RingsF ofF Polynomials 76
24. FactorizationFofFPolynomialsFoverFaFField 79
25. NoncommutativeFExamples 85
26. OrderedF RingsF andF Fields 87
V. IdealsF andF FactorF Rings
27. HomomorphismsFandFFactorFRings 89
28. PrimeFandFMaximalFIdeals 94
,29. GröbnerFBasesFforFIdeals 99
, VI. ExtensionF Fields
30. IntroductionFtoFExtensionFFields 103
31. VectorF Spaces 107
32. AlgebraicF Extensions 111
33. GeometricFConstructions 115
34. FiniteF Fields 116
VII. AdvancedFGroupFTheory
35. IsomorphismFTheorems 117
36. SeriesFofFGroups 119
37. SylowF Theorems 122
38. ApplicationsF ofF theF SylowF Theory 124
39. FreeF AbelianF Groups 128
40. FreeFGroups 130
41. GroupF Presentations 133
VIII. GroupsF inF Topology
42. SimplicialF ComplexesF andF HomologyF Groups 136
43. ComputationsF ofF HomologyFGroups 138
44. MoreFHomologyFComputationsFandFApplications 140
45. HomologicalFAlgebra 144
IX. Factorization
46. UniqueF FactorizationF Domains 148
47. EuclideanF Domains 151
48. GaussianF IntegersF andF MultiplicativeF Norms 154
X. AutomorphismsF andF GaloisF Theory
49. AutomorphismsFofFFields 159
50. TheF IsomorphismF ExtensionF Theorem 164
51. SplittingF Fields 165
52. SeparableFExtensions 167
53. TotallyFInseparableFExtensions 171
54. GaloisF Theory 173
55. IllustrationsFofFGaloisFTheory 176
56. CyclotomicFExtensions 183
57. InsolvabilityF ofF theF Quintic 185
APPENDIXFF MatrixFF Algebra 187
iv
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. SetsF andF Relations 1
I. GroupsF andF Subgroups
2. IntroductionF andF Examples 4
3. BinaryF Operations 7
4. IsomorphicF BinaryF Structures 9
5. Groups 13
6. Subgroups 17
7. CyclicFF Groups 21
8. GeneratorsF andF CayleyF Digraphs 24
II. Permutations,FCosets,FandFDirectFProducts
9. GroupsF ofFPermutations 26
10. Orbits,FCycles,FandFtheFAlternatingFGroups
30
11. CosetsF andFtheF TheoremFofF Lagrange 34
12. DirectF ProductsF andF FinitelyF GeneratedF AbelianF Groups 37
13. PlaneF Isometries 42
III. HomomorphismsF andF FactorF Groups
14. Homomorphisms 44
15. FactorF Groups 49
16. Factor-GroupF ComputationsF andF SimpleF Groups 53
17. GroupFActionFonFaFSet 58
18. ApplicationsFofFG-SetsFtoFCounting 61
IV. RingsF andF Fields
19. RingsFandFFields 63
20. IntegralF Domains 68
21. Fermat’sF andF Euler’sF Theorems 72
22. TheF FieldF ofF QuotientsF ofF anF IntegralF Domain 74
23. RingsF ofF Polynomials 76
24. FactorizationFofFPolynomialsFoverFaFField 79
25. NoncommutativeFExamples 85
26. OrderedF RingsF andF Fields 87
V. IdealsF andF FactorF Rings
27. HomomorphismsFandFFactorFRings 89
28. PrimeFandFMaximalFIdeals 94
,29. GröbnerFBasesFforFIdeals 99
, VI. ExtensionF Fields
30. IntroductionFtoFExtensionFFields 103
31. VectorF Spaces 107
32. AlgebraicF Extensions 111
33. GeometricFConstructions 115
34. FiniteF Fields 116
VII. AdvancedFGroupFTheory
35. IsomorphismFTheorems 117
36. SeriesFofFGroups 119
37. SylowF Theorems 122
38. ApplicationsF ofF theF SylowF Theory 124
39. FreeF AbelianF Groups 128
40. FreeFGroups 130
41. GroupF Presentations 133
VIII. GroupsF inF Topology
42. SimplicialF ComplexesF andF HomologyF Groups 136
43. ComputationsF ofF HomologyFGroups 138
44. MoreFHomologyFComputationsFandFApplications 140
45. HomologicalFAlgebra 144
IX. Factorization
46. UniqueF FactorizationF Domains 148
47. EuclideanF Domains 151
48. GaussianF IntegersF andF MultiplicativeF Norms 154
X. AutomorphismsF andF GaloisF Theory
49. AutomorphismsFofFFields 159
50. TheF IsomorphismF ExtensionF Theorem 164
51. SplittingF Fields 165
52. SeparableFExtensions 167
53. TotallyFInseparableFExtensions 171
54. GaloisF Theory 173
55. IllustrationsFofFGaloisFTheory 176
56. CyclotomicFExtensions 183
57. InsolvabilityF ofF theF Quintic 185
APPENDIXFF MatrixFF Algebra 187
iv
