SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsaa andaa Relations 1
I. Groupsa a anda a Subgroups
2. Introductiona a anda a Examples 4
3. Binarya a Operations 7
4. Isomorphica a Binarya a Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclicaaa a Groups 21
8. Generatorsa a anda a Cayleya a Digraphs 24
II. Permutations,aaCosets,aaandaaDirectaaProducts
9. Groupsaa ofaaPermutations 26
10. Orbits,aaCycles,aaandaatheaaAlternatingaaGroups
30
11. Cosetsaa andaatheaa Theoremaa ofaa Lagrange 34
12. Directa a Productsa a anda a Finitelya a Generateda a Abeliana a Groups 37
13. Planea a Isometries 42
III. Homomorphismsa a anda a Factora a Groups
14. Homomorphisms 44
15. Factora a Groups 49
16. Factor-Groupa a Computationsa a anda a Simplea a Groups 53
17. GroupaaActionaaonaaaaaSet58
18. ApplicationsaaofaaG-SetsaatoaaCounting 61
IV. Ringsa a anda a Fields
19. RingsaaandaaFields 63
20. Integrala a Domains 68
21. Fermat’sa a anda a Euler’sa a Theorems 72
22. Thea a Fielda a ofa a Quotientsa a ofa a ana a Integrala a Domain 74
23. Ringsa a ofa a Polynomials 76
24. FactorizationaaofaaPolynomialsaaoveraaaaaField 79
25. NoncommutativeaaExamples 85
26. Ordereda a Ringsa a anda a Fields 87
V. Idealsa a anda a Factora a Rings
27. HomomorphismsaaandaaFactoraaRings 89
28. PrimeaaandaaMaximalaaIdeals 94
,29. GröbneraaBasesaaforaaIdeals 99
, VI. Extensiona a Fields
30. IntroductionaatoaaExtensionaaFields 103
31. Vectora a Spaces 107
32. Algebraica a Extensions 111
33. GeometricaaConstructions 115
34. Finitea a Fields 116
VII. AdvancedaaGroupaaTheory
35. IsomorphismaaTheorems 117
36. SeriesaaofaaGroups 119
37. Sylowa a Theorems 122
38. Applicationsa a ofa a thea a Sylowa a Theory124
39. Freea a Abeliana a Groups 128
40. FreeaaGroups 130
41. Groupa a Presentations 133
VIII. Groupsa a ina a Topology
42. Simpliciala a Complexesa a anda a Homologya a Groups 136
43. Computationsaa ofaa HomologyaaGroups 138
44. MoreaaHomologyaaComputationsaaandaaApplications 140
45. HomologicalaaAlgebra 144
IX. Factorization
46. Uniquea a Factorizationa a Domains 148
47. Euclideana a Domains 151
48. Gaussiana a Integersa a anda a Multiplicativea a Norms154
X. Automorphismsa a anda a Galoisa a Theory
49. AutomorphismsaaofaaFields 159
50. Thea a Isomorphisma a Extensiona a Theorem 164
51. Splittinga a Fields 165
52. SeparableaaExtensions 167
53. TotallyaaInseparableaaExtensions 171
54. Galoisa a Theory 173
55. IllustrationsaaofaaGaloisaaTheory 176
56. CyclotomicaaExtensions 183
57. Insolvabilityaa ofa a thea a Quintic 185
APPENDIXaaa a Matrixaaaa Algebra 187
iv
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsaa andaa Relations 1
I. Groupsa a anda a Subgroups
2. Introductiona a anda a Examples 4
3. Binarya a Operations 7
4. Isomorphica a Binarya a Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclicaaa a Groups 21
8. Generatorsa a anda a Cayleya a Digraphs 24
II. Permutations,aaCosets,aaandaaDirectaaProducts
9. Groupsaa ofaaPermutations 26
10. Orbits,aaCycles,aaandaatheaaAlternatingaaGroups
30
11. Cosetsaa andaatheaa Theoremaa ofaa Lagrange 34
12. Directa a Productsa a anda a Finitelya a Generateda a Abeliana a Groups 37
13. Planea a Isometries 42
III. Homomorphismsa a anda a Factora a Groups
14. Homomorphisms 44
15. Factora a Groups 49
16. Factor-Groupa a Computationsa a anda a Simplea a Groups 53
17. GroupaaActionaaonaaaaaSet58
18. ApplicationsaaofaaG-SetsaatoaaCounting 61
IV. Ringsa a anda a Fields
19. RingsaaandaaFields 63
20. Integrala a Domains 68
21. Fermat’sa a anda a Euler’sa a Theorems 72
22. Thea a Fielda a ofa a Quotientsa a ofa a ana a Integrala a Domain 74
23. Ringsa a ofa a Polynomials 76
24. FactorizationaaofaaPolynomialsaaoveraaaaaField 79
25. NoncommutativeaaExamples 85
26. Ordereda a Ringsa a anda a Fields 87
V. Idealsa a anda a Factora a Rings
27. HomomorphismsaaandaaFactoraaRings 89
28. PrimeaaandaaMaximalaaIdeals 94
,29. GröbneraaBasesaaforaaIdeals 99
, VI. Extensiona a Fields
30. IntroductionaatoaaExtensionaaFields 103
31. Vectora a Spaces 107
32. Algebraica a Extensions 111
33. GeometricaaConstructions 115
34. Finitea a Fields 116
VII. AdvancedaaGroupaaTheory
35. IsomorphismaaTheorems 117
36. SeriesaaofaaGroups 119
37. Sylowa a Theorems 122
38. Applicationsa a ofa a thea a Sylowa a Theory124
39. Freea a Abeliana a Groups 128
40. FreeaaGroups 130
41. Groupa a Presentations 133
VIII. Groupsa a ina a Topology
42. Simpliciala a Complexesa a anda a Homologya a Groups 136
43. Computationsaa ofaa HomologyaaGroups 138
44. MoreaaHomologyaaComputationsaaandaaApplications 140
45. HomologicalaaAlgebra 144
IX. Factorization
46. Uniquea a Factorizationa a Domains 148
47. Euclideana a Domains 151
48. Gaussiana a Integersa a anda a Multiplicativea a Norms154
X. Automorphismsa a anda a Galoisa a Theory
49. AutomorphismsaaofaaFields 159
50. Thea a Isomorphisma a Extensiona a Theorem 164
51. Splittinga a Fields 165
52. SeparableaaExtensions 167
53. TotallyaaInseparableaaExtensions 171
54. Galoisa a Theory 173
55. IllustrationsaaofaaGaloisaaTheory 176
56. CyclotomicaaExtensions 183
57. Insolvabilityaa ofa a thea a Quintic 185
APPENDIXaaa a Matrixaaaa Algebra 187
iv
