SOLUTION MANUAL z
First Course in Abstract Algebra A
z z z z z z
zz 8th Edition by John B. Fraleigh
z z z z z z z
z All Chapters Full Complete
z z z
, CONTENTS
1. Sets z and zRelations 1
I. Groups z and z Subgroups
2. Introduction z and z Examples 4
3. Binary z Operations 7
4. Isomorphic z Binary z Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic z z Groups 21
8. Generators z and z Cayley z Digraphs 24
II. Permutations, zCosets, zand zDirect zProducts
9. Groups zof zPermutations 26
10. Orbits, zCycles, zand zthe zAlternating zGroups
30
11. Cosets zand zthe zTheorem zof zLagrange 34
12. Direct z Products z and z Finitely z Generated z Abelian z Groups 37
13. Plane z Isometries 42
III. Homomorphisms z and z Factor z Groups
14. Homomorphisms 44
15. Factor z Groups 49
16. Factor-Group z Computations z and z Simple z Groups 53
17. Group zAction zon za zSet 58
18. Applications zof zG-Sets zto zCounting 61
IV. Rings z and z Fields
19. Rings zand zFields 63
20. Integral z Domains 68
21. Fermat’s z and z Euler’s z Theorems 72
22. The z Field z of z Quotients z of z an z Integral z Domain 74
23. Rings z of z Polynomials 76
24. Factorization zof zPolynomials zover za zField 79
25. Noncommutative zExamples 85
26. Ordered z Rings z and z Fields 87
V. Ideals z and z Factor z Rings
27. Homomorphisms zand zFactor zRings 89
28. Prime zand zMaximal zIdeals 94
,29. Gröbner zBases zfor zIdeals 99
, VI. Extension z Fields
30. Introduction zto zExtension zFields 103
31. Vector z Spaces 107
32. Algebraic z Extensions 111
33. Geometric zConstructions 115
34. Finite z Fields 116
VII. Advanced zGroup zTheory
35. Isomorphism zTheorems 117
36. Series zof zGroups 119
37. Sylow z Theorems 122
38. Applications z of z the z Sylow z Theory 124
39. Free z Abelian z Groups 128
40. Free zGroups 130
41. Group z Presentations 133
VIII. Groups z in z Topology
42. Simplicial z Complexes z and z Homology z Groups 136
43. Computations zof zHomology zGroups 138
44. More zHomology zComputations zand zApplications 140
45. Homological zAlgebra 144
IX. Factorization
46. Unique z Factorization z Domains 148
47. Euclidean z Domains 151
48. Gaussian z Integers z and z Multiplicative z Norms 154
X. Automorphisms z and z Galois z Theory
49. Automorphisms zof zFields 159
50. The z Isomorphism z Extension z Theorem 164
51. Splitting z Fields 165
52. Separable zExtensions 167
53. Totally zInseparable zExtensions 171
54. Galois z Theory 173
55. Illustrations zof zGalois zTheory 176
56. CyclotomiczExtensions 183
57. Insolvability z of z the z Quintic 185
APPENDIX z z Matrix z z Algebra 187
iv
First Course in Abstract Algebra A
z z z z z z
zz 8th Edition by John B. Fraleigh
z z z z z z z
z All Chapters Full Complete
z z z
, CONTENTS
1. Sets z and zRelations 1
I. Groups z and z Subgroups
2. Introduction z and z Examples 4
3. Binary z Operations 7
4. Isomorphic z Binary z Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic z z Groups 21
8. Generators z and z Cayley z Digraphs 24
II. Permutations, zCosets, zand zDirect zProducts
9. Groups zof zPermutations 26
10. Orbits, zCycles, zand zthe zAlternating zGroups
30
11. Cosets zand zthe zTheorem zof zLagrange 34
12. Direct z Products z and z Finitely z Generated z Abelian z Groups 37
13. Plane z Isometries 42
III. Homomorphisms z and z Factor z Groups
14. Homomorphisms 44
15. Factor z Groups 49
16. Factor-Group z Computations z and z Simple z Groups 53
17. Group zAction zon za zSet 58
18. Applications zof zG-Sets zto zCounting 61
IV. Rings z and z Fields
19. Rings zand zFields 63
20. Integral z Domains 68
21. Fermat’s z and z Euler’s z Theorems 72
22. The z Field z of z Quotients z of z an z Integral z Domain 74
23. Rings z of z Polynomials 76
24. Factorization zof zPolynomials zover za zField 79
25. Noncommutative zExamples 85
26. Ordered z Rings z and z Fields 87
V. Ideals z and z Factor z Rings
27. Homomorphisms zand zFactor zRings 89
28. Prime zand zMaximal zIdeals 94
,29. Gröbner zBases zfor zIdeals 99
, VI. Extension z Fields
30. Introduction zto zExtension zFields 103
31. Vector z Spaces 107
32. Algebraic z Extensions 111
33. Geometric zConstructions 115
34. Finite z Fields 116
VII. Advanced zGroup zTheory
35. Isomorphism zTheorems 117
36. Series zof zGroups 119
37. Sylow z Theorems 122
38. Applications z of z the z Sylow z Theory 124
39. Free z Abelian z Groups 128
40. Free zGroups 130
41. Group z Presentations 133
VIII. Groups z in z Topology
42. Simplicial z Complexes z and z Homology z Groups 136
43. Computations zof zHomology zGroups 138
44. More zHomology zComputations zand zApplications 140
45. Homological zAlgebra 144
IX. Factorization
46. Unique z Factorization z Domains 148
47. Euclidean z Domains 151
48. Gaussian z Integers z and z Multiplicative z Norms 154
X. Automorphisms z and z Galois z Theory
49. Automorphisms zof zFields 159
50. The z Isomorphism z Extension z Theorem 164
51. Splitting z Fields 165
52. Separable zExtensions 167
53. Totally zInseparable zExtensions 171
54. Galois z Theory 173
55. Illustrations zof zGalois zTheory 176
56. CyclotomiczExtensions 183
57. Insolvability z of z the z Quintic 185
APPENDIX z z Matrix z z Algebra 187
iv
