SOLUTION MANUAL f
First Course in Abstract Algebra A
f f f f f f
f f 8th Edition by John B. Fraleigh
f f f f f f f
f All Chapters Full Complete
f f f
, CONTENTS
1. Sets f and f Relations 1
I. Groups and Subgroups
f f
2. Introduction f and f Examples 4
3. Binary f Operations 7
4. Isomorphic f Binary f Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic f f Groups 21
8. Generators f and f Cayley f Digraphs 24
II. Permutations, Cosets, and Direct Products
f f f f
9. Groups f of fPermutations 26
10. Orbits, fCycles, fand fthe fAlternating fGroups
30
11. Cosets fand fthe fTheorem f of fLagrange 34
12. Direct f Products f and f Finitely f Generated f Abelian f Groups 37
13. Plane f Isometries 42
III. Homomorphisms and Factor Groups f f f
14. Homomorphisms 44
15. Factor f Groups 49
16. Factor-Group f Computations f and f Simple f Groups 53
17. Group fAction fon fa fSet 58
18. Applications fof fG-Sets fto fCounting 61
IV. Rings and Fieldsf f
19. Rings fand fFields 63
20. Integral f Domains 68
21. Fermat’s f and f Euler’s f Theorems 72
22. The f Field f of f Quotients f of f an f Integral f Domain 74
23. Rings f of f Polynomials 76
24. Factorization fof fPolynomials fover fa fField 79
25. Noncommutative fExamples 85
26. Ordered f Rings f and f Fields 87
V. Ideals and Factor Rings
f f f
27. Homomorphisms fand fFactor fRings 89
28. Prime fand fMaximal fIdeals 94
,29. Gröbner fBases ffor fIdeals 99
, VI. Extension Fields f
30. Introduction fto fExtension fFields 103
31. Vector f Spaces 107
32. Algebraic f Extensions 111
33. Geometric fConstructions 115
34. Finite f Fields 116
VII. Advanced Group Theory
f f
35. Isomorphism fTheorems 117
36. Series fof fGroups 119
37. Sylow f Theorems 122
38. Applications f of f the f Sylow f Theory 124
39. Free f Abelian f Groups 128
40. Free fGroups 130
41. Group f Presentations 133
VIII. Groups in Topology
f f
42. Simplicial f Complexes f and f Homology f Groups 136
43. Computations fof fHomology fGroups 138
44. More fHomology fComputations fand fApplications 140
45. Homological fAlgebra 144
IX. Factorization
46. Unique f Factorization f Domains 148
47. Euclidean f Domains 151
48. Gaussian f Integers f and f Multiplicative f Norms 154
X. Automorphisms and Galois Theory
f f f
49. Automorphisms fof fFields 159
50. The f Isomorphism f Extension f Theorem 164
51. Splitting f Fields 165
52. Separable fExtensions 167
53. Totally fInseparable fExtensions 171
54. Galois f Theory 173
55. Illustrations fof fGalois fTheory 176
56. CyclotomicfExtensions 183
57. Insolvability f of f the f Quintic 185
APPENDIX f f Matrix f f Algebra 187
iv
First Course in Abstract Algebra A
f f f f f f
f f 8th Edition by John B. Fraleigh
f f f f f f f
f All Chapters Full Complete
f f f
, CONTENTS
1. Sets f and f Relations 1
I. Groups and Subgroups
f f
2. Introduction f and f Examples 4
3. Binary f Operations 7
4. Isomorphic f Binary f Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic f f Groups 21
8. Generators f and f Cayley f Digraphs 24
II. Permutations, Cosets, and Direct Products
f f f f
9. Groups f of fPermutations 26
10. Orbits, fCycles, fand fthe fAlternating fGroups
30
11. Cosets fand fthe fTheorem f of fLagrange 34
12. Direct f Products f and f Finitely f Generated f Abelian f Groups 37
13. Plane f Isometries 42
III. Homomorphisms and Factor Groups f f f
14. Homomorphisms 44
15. Factor f Groups 49
16. Factor-Group f Computations f and f Simple f Groups 53
17. Group fAction fon fa fSet 58
18. Applications fof fG-Sets fto fCounting 61
IV. Rings and Fieldsf f
19. Rings fand fFields 63
20. Integral f Domains 68
21. Fermat’s f and f Euler’s f Theorems 72
22. The f Field f of f Quotients f of f an f Integral f Domain 74
23. Rings f of f Polynomials 76
24. Factorization fof fPolynomials fover fa fField 79
25. Noncommutative fExamples 85
26. Ordered f Rings f and f Fields 87
V. Ideals and Factor Rings
f f f
27. Homomorphisms fand fFactor fRings 89
28. Prime fand fMaximal fIdeals 94
,29. Gröbner fBases ffor fIdeals 99
, VI. Extension Fields f
30. Introduction fto fExtension fFields 103
31. Vector f Spaces 107
32. Algebraic f Extensions 111
33. Geometric fConstructions 115
34. Finite f Fields 116
VII. Advanced Group Theory
f f
35. Isomorphism fTheorems 117
36. Series fof fGroups 119
37. Sylow f Theorems 122
38. Applications f of f the f Sylow f Theory 124
39. Free f Abelian f Groups 128
40. Free fGroups 130
41. Group f Presentations 133
VIII. Groups in Topology
f f
42. Simplicial f Complexes f and f Homology f Groups 136
43. Computations fof fHomology fGroups 138
44. More fHomology fComputations fand fApplications 140
45. Homological fAlgebra 144
IX. Factorization
46. Unique f Factorization f Domains 148
47. Euclidean f Domains 151
48. Gaussian f Integers f and f Multiplicative f Norms 154
X. Automorphisms and Galois Theory
f f f
49. Automorphisms fof fFields 159
50. The f Isomorphism f Extension f Theorem 164
51. Splitting f Fields 165
52. Separable fExtensions 167
53. Totally fInseparable fExtensions 171
54. Galois f Theory 173
55. Illustrations fof fGalois fTheory 176
56. CyclotomicfExtensions 183
57. Insolvability f of f the f Quintic 185
APPENDIX f f Matrix f f Algebra 187
iv
