SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsdc anddc Relations 1
I. Groupsd c andd c Subgroups
2. Introductiondc anddc Examples 4
3. Binaryd c Operations 7
4. Isomorphicd c Binaryd c Structures9
5. Groups 13
6. Subgroups 17
7. Cyclicdc dc Groups 21
8. Generatorsdc andd c Cayleydc Digraphs 24
II. Permutations,dc Cosets,dc anddc Directdc Products
9. Groupsdc ofdc Permutations 26
10. Orbits,dc Cycles,dc anddc thedc Alternatingdc
Groups 30
11. Cosetsdc anddc thedc Theoremdc ofdc Lagrange 34
12. Directd c Productsd c andd c Finitelyd c Generatedd c Abeliand c Groups 37
13. Planed c Isometries 42
III. Homomorphismsd c andd c Factord c Groups
14. Homomorphisms 44
15. Factord c Groups 49
16. Factor-Groupd c Computationsd c andd c Simpled c Groups 53
17. Groupdc Actiondc ondc adc Set 58
18. Applicationsdc ofdc G-Setsdc todc Counting 61
IV. Ringsd c andd c Fields
19. Ringsdc anddc Fields 63
20. Integraldc Domains 68
21. Fermat’sd c andd c Euler’sd c Theorems 72
22. Thed c Fieldd c ofd c Quotientsd c ofd c and c Integrald c Domain 74
23. Ringsd c ofd c Polynomials76
24. Factorizationdc ofdc Polynomialsdc overdc adc Field 79
25. Noncommutativedc Examples 85
26. Orderedd c Ringsd c andd c Fields 87
V. Idealsd c andd c Factord c Rings
27. Homomorphismsdc anddc Factordc Rings89
28. Primedc anddc Maximaldc Ideals 94
,29. Gröbnerdc Basesdc fordc Ideals 99
, VI. Extensiond c Fields
30. Introductiondc todc Extensiondc Fields 103
31. Vectord c Spaces 107
32. Algebraicd c Extensions 111
33. GeometricdcConstructions 115
34. Finitedc Fields 116
VII. Advanceddc Groupdc Theory
35. IsomorphismdcTheorems 117
36. Seriesdc ofdc Groups 119
37. Sylowdc Theorems 122
38. Applicationsd c ofd c thed c Sylowd c Theory 124
39. Freed c Abeliand c Groups 128
40. Freedc Groups 130
41. Groupdc Presentations 133
VIII. Groupsd c ind c Topology
42. Simplicialdc Complexesd c andd c Homologyd c Groups 136
43. Computationsdc ofdc Homologydc Groups 138
44. Moredc Homologydc Computationsdc anddc Applications 140
45. Homologicaldc Algebra 144
IX. Factorization
46. Uniquedc Factorizationd c Domains 148
47. Euclideand c Domains 151
48. Gaussiand c Integersd c andd c Multiplicatived c Norms 154
X. Automorphismsd c andd c Galoisd c Theory
49. Automorphismsdc ofdc Fields 159
50. Thed c Isomorphismd c Extensiond c Theorem 164
51. Splittingdc Fields 165
52. SeparabledcExtensions 167
53. Totallydc Inseparabledc Extensions 171
54. Galoisd c Theory 173
55. IllustrationsdcofdcGaloisdc Theory 176
56. CyclotomicdcExtensions 183
57. Insolvabilitydc ofdc thed c Quintic 185
APPENDIXdc d c Matrixdc dc Algebra 187
iv
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Setsdc anddc Relations 1
I. Groupsd c andd c Subgroups
2. Introductiondc anddc Examples 4
3. Binaryd c Operations 7
4. Isomorphicd c Binaryd c Structures9
5. Groups 13
6. Subgroups 17
7. Cyclicdc dc Groups 21
8. Generatorsdc andd c Cayleydc Digraphs 24
II. Permutations,dc Cosets,dc anddc Directdc Products
9. Groupsdc ofdc Permutations 26
10. Orbits,dc Cycles,dc anddc thedc Alternatingdc
Groups 30
11. Cosetsdc anddc thedc Theoremdc ofdc Lagrange 34
12. Directd c Productsd c andd c Finitelyd c Generatedd c Abeliand c Groups 37
13. Planed c Isometries 42
III. Homomorphismsd c andd c Factord c Groups
14. Homomorphisms 44
15. Factord c Groups 49
16. Factor-Groupd c Computationsd c andd c Simpled c Groups 53
17. Groupdc Actiondc ondc adc Set 58
18. Applicationsdc ofdc G-Setsdc todc Counting 61
IV. Ringsd c andd c Fields
19. Ringsdc anddc Fields 63
20. Integraldc Domains 68
21. Fermat’sd c andd c Euler’sd c Theorems 72
22. Thed c Fieldd c ofd c Quotientsd c ofd c and c Integrald c Domain 74
23. Ringsd c ofd c Polynomials76
24. Factorizationdc ofdc Polynomialsdc overdc adc Field 79
25. Noncommutativedc Examples 85
26. Orderedd c Ringsd c andd c Fields 87
V. Idealsd c andd c Factord c Rings
27. Homomorphismsdc anddc Factordc Rings89
28. Primedc anddc Maximaldc Ideals 94
,29. Gröbnerdc Basesdc fordc Ideals 99
, VI. Extensiond c Fields
30. Introductiondc todc Extensiondc Fields 103
31. Vectord c Spaces 107
32. Algebraicd c Extensions 111
33. GeometricdcConstructions 115
34. Finitedc Fields 116
VII. Advanceddc Groupdc Theory
35. IsomorphismdcTheorems 117
36. Seriesdc ofdc Groups 119
37. Sylowdc Theorems 122
38. Applicationsd c ofd c thed c Sylowd c Theory 124
39. Freed c Abeliand c Groups 128
40. Freedc Groups 130
41. Groupdc Presentations 133
VIII. Groupsd c ind c Topology
42. Simplicialdc Complexesd c andd c Homologyd c Groups 136
43. Computationsdc ofdc Homologydc Groups 138
44. Moredc Homologydc Computationsdc anddc Applications 140
45. Homologicaldc Algebra 144
IX. Factorization
46. Uniquedc Factorizationd c Domains 148
47. Euclideand c Domains 151
48. Gaussiand c Integersd c andd c Multiplicatived c Norms 154
X. Automorphismsd c andd c Galoisd c Theory
49. Automorphismsdc ofdc Fields 159
50. Thed c Isomorphismd c Extensiond c Theorem 164
51. Splittingdc Fields 165
52. SeparabledcExtensions 167
53. Totallydc Inseparabledc Extensions 171
54. Galoisd c Theory 173
55. IllustrationsdcofdcGaloisdc Theory 176
56. CyclotomicdcExtensions 183
57. Insolvabilitydc ofdc thed c Quintic 185
APPENDIXdc d c Matrixdc dc Algebra 187
iv
