SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsd andd Relations 1
I. Groups and Subgroups
d d
2. Introductiond andd Examples 4
3. Binaryd Operations 7
4. Isomorphicd Binaryd Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclicdd Groups 21
8. Generatorsd andd Cayleyd Digraphs 24
II. Permutations, Cosets, and Direct Products
d d d d
9. Groupsd ofdPermutations 26
10. Orbits,dCycles,danddthedAlternatingdGroups
30
11. Cosetsd anddthed Theoremdofd Lagrange 34
12. Directd Productsd andd Finitelyd Generatedd Abeliand Groups 37
13. Planed Isometries 42
III. Homomorphisms and Factor Groupsd d d
14. Homomorphisms 44
15. Factord Groups 49
16. Factor-Groupd Computationsd andd Simpled Groups 53
17. GroupdActiondondadSet 58
18. ApplicationsdofdG-SetsdtodCounting 61
IV. Rings and Fields
d d
19. RingsdanddFields 63
20. Integrald Domains 68
21. Fermat’sd andd Euler’sd Theorems 72
22. Thed Fieldd ofd Quotientsd ofd and Integrald Domain 74
23. Ringsd ofd Polynomials 76
24. FactorizationdofdPolynomialsdoverdadField 79
25. NoncommutativedExamples 85
26. Orderedd Ringsd andd Fields 87
V. Ideals and Factor Rings
d d d
27. HomomorphismsdanddFactordRings 89
28. PrimedanddMaximaldIdeals 94
,29. GröbnerdBasesdfordIdeals 99
, VI. Extension Fields d
30. IntroductiondtodExtensiondFields 103
31. Vectord Spaces 107
32. Algebraicd Extensions 111
33. GeometricdConstructions 115
34. Finited Fields 116
VII. Advanced Group Theory d d
35. IsomorphismdTheorems 117
36. SeriesdofdGroups 119
37. Sylowd Theorems 122
38. Applicationsd ofd thed Sylowd Theory 124
39. Freed Abeliand Groups 128
40. FreedGroups 130
41. Groupd Presentations 133
VIII. Groups in Topologyd d
42. Simpliciald Complexesd andd Homologyd Groups 136
43. Computationsd ofd HomologydGroups 138
44. MoredHomologydComputationsdanddApplications 140
45. HomologicaldAlgebra 144
IX. Factorization
46. Uniqued Factorizationd Domains 148
47. Euclideand Domains 151
48. Gaussiand Integersd andd Multiplicatived Norms 154
X. Automorphisms and Galois Theory
d d d
49. AutomorphismsdofdFields 159
50. Thed Isomorphismd Extensiond Theorem 164
51. Splittingd Fields 165
52. SeparabledExtensions 167
53. TotallydInseparabledExtensions 171
54. Galoisd Theory 173
55. IllustrationsdofdGaloisdTheory 176
56. CyclotomicdExtensions 183
57. Insolvabilityd ofd thed Quintic 185
APPENDIXdd Matrixdd Algebra 187
iv
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsd andd Relations 1
I. Groups and Subgroups
d d
2. Introductiond andd Examples 4
3. Binaryd Operations 7
4. Isomorphicd Binaryd Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclicdd Groups 21
8. Generatorsd andd Cayleyd Digraphs 24
II. Permutations, Cosets, and Direct Products
d d d d
9. Groupsd ofdPermutations 26
10. Orbits,dCycles,danddthedAlternatingdGroups
30
11. Cosetsd anddthed Theoremdofd Lagrange 34
12. Directd Productsd andd Finitelyd Generatedd Abeliand Groups 37
13. Planed Isometries 42
III. Homomorphisms and Factor Groupsd d d
14. Homomorphisms 44
15. Factord Groups 49
16. Factor-Groupd Computationsd andd Simpled Groups 53
17. GroupdActiondondadSet 58
18. ApplicationsdofdG-SetsdtodCounting 61
IV. Rings and Fields
d d
19. RingsdanddFields 63
20. Integrald Domains 68
21. Fermat’sd andd Euler’sd Theorems 72
22. Thed Fieldd ofd Quotientsd ofd and Integrald Domain 74
23. Ringsd ofd Polynomials 76
24. FactorizationdofdPolynomialsdoverdadField 79
25. NoncommutativedExamples 85
26. Orderedd Ringsd andd Fields 87
V. Ideals and Factor Rings
d d d
27. HomomorphismsdanddFactordRings 89
28. PrimedanddMaximaldIdeals 94
,29. GröbnerdBasesdfordIdeals 99
, VI. Extension Fields d
30. IntroductiondtodExtensiondFields 103
31. Vectord Spaces 107
32. Algebraicd Extensions 111
33. GeometricdConstructions 115
34. Finited Fields 116
VII. Advanced Group Theory d d
35. IsomorphismdTheorems 117
36. SeriesdofdGroups 119
37. Sylowd Theorems 122
38. Applicationsd ofd thed Sylowd Theory 124
39. Freed Abeliand Groups 128
40. FreedGroups 130
41. Groupd Presentations 133
VIII. Groups in Topologyd d
42. Simpliciald Complexesd andd Homologyd Groups 136
43. Computationsd ofd HomologydGroups 138
44. MoredHomologydComputationsdanddApplications 140
45. HomologicaldAlgebra 144
IX. Factorization
46. Uniqued Factorizationd Domains 148
47. Euclideand Domains 151
48. Gaussiand Integersd andd Multiplicatived Norms 154
X. Automorphisms and Galois Theory
d d d
49. AutomorphismsdofdFields 159
50. Thed Isomorphismd Extensiond Theorem 164
51. Splittingd Fields 165
52. SeparabledExtensions 167
53. TotallydInseparabledExtensions 171
54. Galoisd Theory 173
55. IllustrationsdofdGaloisdTheory 176
56. CyclotomicdExtensions 183
57. Insolvabilityd ofd thed Quintic 185
APPENDIXdd Matrixdd Algebra 187
iv
