SOLUTION MANUAL
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Sets63 and63 Relations 1
I. Groups6 3 and6 3 Subgroups
2. Introduction63 and63 Examples 4
3. Binary6 3 Operations 7
4. Isomorphic6 3 Binary6 3 Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic6363 Groups 21
8. Generators63 and63 Cayley63 Digraphs 24
II. Permutations,63Cosets,63and63Direct63Products
9. Groups63 of63Permutations 26
10. Orbits,63Cycles,63and63the63Alternating63Group
s 30
11. Cosets63 and63the63 Theorem63 of63 Lagrange 34
12. Direct6 3 Products6 3 and6 3 Finitely6 3 Generated6 3 Abelian6 3 Groups 37
13. Plane6 3 Isometries 42
III. Homomorphisms6 3 and6 3 Factor6 3 Groups
14. Homomorphisms 44
15. Factor63 Groups 49
16. Factor-Group6 3 Computations6 3 and6 3 Simple6 3 Groups 53
17. Group63Action63on63a63Set 58
18. Applications63of63G-Sets63to63Counting 61
IV. Rings6 3 and6 3 Fields
19. Rings63and63Fields 63
20. Integral63 Domains 68
21. Fermat’s6 3 and6 3 Euler’s6 3 Theorems 72
22. The6 3 Field6 3 of6 3 Quotients6 3 of6 3 an6 3 Integral6 3 Domain 74
23. Rings6 3 of6 3 Polynomials 76
24. Factorization63of63Polynomials63over63a63Field 79
25. Noncommutative63Examples 85
26. Ordered6 3 Rings6 3 and6 3 Fields 87
V. Ideals6 3 and6 3 Factor6 3 Rings
27. Homomorphisms63and63Factor63Rings 89
28. Prime63and63Maximal63Ideals 94
,29. Gröbner63Bases63for63Ideals 99
, VI. Extension6 3 Fields
30. Introduction63to63Extension63Fields 103
31. Vector6 3 Spaces 107
32. Algebraic6 3 Extensions 111
33. Geometric63Constructions 115
34. Finite63 Fields 116
VII. Advanced63Group63Theory
35. Isomorphism63Theorems 117
36. Series63of63Groups 119
37. Sylow63 Theorems 122
38. Applications6 3 of6 3 the6 3 Sylow6 3 Theory 124
39. Free6 3 Abelian6 3 Groups 128
40. Free63Groups 130
41. Group63 Presentations 133
VIII. Groups6 3 in6 3 Topology
42. Simplicial63 Complexes6 3 and6 3 Homology6 3 Groups 136
43. Computations63of63 Homology63Groups 138
44. More63Homology63Computations63and63Applications 140
45. Homological63Algebra 144
IX. Factorization
46. Unique63 Factorization6 3 Domains 148
47. Euclidean6 3 Domains 151
48. Gaussian6 3 Integers6 3 and6 3 Multiplicative6 3 Norms 154
X. Automorphisms6 3 and6 3 Galois6 3 Theory
49. Automorphisms63of63Fields 159
50. The6 3 Isomorphism6 3 Extension6 3 Theorem 164
51. Splitting63 Fields 165
52. Separable63Extensions 167
53. Totally63Inseparable63Extensions 171
54. Galois6 3 Theory 173
55. Illustrations63of63Galois63Theory 176
56. Cyclotomic63Extensions 183
57. Insolvability63 of63 the6 3 Quintic 185
APPENDIX636 3 Matrix6363 Algebra 187
iv
First Course in Abstract Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Sets63 and63 Relations 1
I. Groups6 3 and6 3 Subgroups
2. Introduction63 and63 Examples 4
3. Binary6 3 Operations 7
4. Isomorphic6 3 Binary6 3 Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic6363 Groups 21
8. Generators63 and63 Cayley63 Digraphs 24
II. Permutations,63Cosets,63and63Direct63Products
9. Groups63 of63Permutations 26
10. Orbits,63Cycles,63and63the63Alternating63Group
s 30
11. Cosets63 and63the63 Theorem63 of63 Lagrange 34
12. Direct6 3 Products6 3 and6 3 Finitely6 3 Generated6 3 Abelian6 3 Groups 37
13. Plane6 3 Isometries 42
III. Homomorphisms6 3 and6 3 Factor6 3 Groups
14. Homomorphisms 44
15. Factor63 Groups 49
16. Factor-Group6 3 Computations6 3 and6 3 Simple6 3 Groups 53
17. Group63Action63on63a63Set 58
18. Applications63of63G-Sets63to63Counting 61
IV. Rings6 3 and6 3 Fields
19. Rings63and63Fields 63
20. Integral63 Domains 68
21. Fermat’s6 3 and6 3 Euler’s6 3 Theorems 72
22. The6 3 Field6 3 of6 3 Quotients6 3 of6 3 an6 3 Integral6 3 Domain 74
23. Rings6 3 of6 3 Polynomials 76
24. Factorization63of63Polynomials63over63a63Field 79
25. Noncommutative63Examples 85
26. Ordered6 3 Rings6 3 and6 3 Fields 87
V. Ideals6 3 and6 3 Factor6 3 Rings
27. Homomorphisms63and63Factor63Rings 89
28. Prime63and63Maximal63Ideals 94
,29. Gröbner63Bases63for63Ideals 99
, VI. Extension6 3 Fields
30. Introduction63to63Extension63Fields 103
31. Vector6 3 Spaces 107
32. Algebraic6 3 Extensions 111
33. Geometric63Constructions 115
34. Finite63 Fields 116
VII. Advanced63Group63Theory
35. Isomorphism63Theorems 117
36. Series63of63Groups 119
37. Sylow63 Theorems 122
38. Applications6 3 of6 3 the6 3 Sylow6 3 Theory 124
39. Free6 3 Abelian6 3 Groups 128
40. Free63Groups 130
41. Group63 Presentations 133
VIII. Groups6 3 in6 3 Topology
42. Simplicial63 Complexes6 3 and6 3 Homology6 3 Groups 136
43. Computations63of63 Homology63Groups 138
44. More63Homology63Computations63and63Applications 140
45. Homological63Algebra 144
IX. Factorization
46. Unique63 Factorization6 3 Domains 148
47. Euclidean6 3 Domains 151
48. Gaussian6 3 Integers6 3 and6 3 Multiplicative6 3 Norms 154
X. Automorphisms6 3 and6 3 Galois6 3 Theory
49. Automorphisms63of63Fields 159
50. The6 3 Isomorphism6 3 Extension6 3 Theorem 164
51. Splitting63 Fields 165
52. Separable63Extensions 167
53. Totally63Inseparable63Extensions 171
54. Galois6 3 Theory 173
55. Illustrations63of63Galois63Theory 176
56. Cyclotomic63Extensions 183
57. Insolvability63 of63 the6 3 Quintic 185
APPENDIX636 3 Matrix6363 Algebra 187
iv
