SOLUTION MANUAL
First Course in Abstract
Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Sets;, and; , Relations; , ; , 1
I. Groups; , and; , Subgroups
2. Introduction; , and; , Examples; , 4
3. Binary; , Operations; , 7
4. Isomorphic; , Binary; , Structures;, 9
5. Groups 13
6. Subgroups 17
7. Cyclic; , Groups; , 21
8. Generators; , and; , Cayley; , Digraphs 24
II. Permutations,; , Cosets,; , and; , Direct; , Products
9. Groups; , of; , Permutations; , 26
10. Orbits,;,Cycles,;,and;,the;,Alternating;,Group
s;,30
11. Cosets; , and; , the; , Theorem; , of; , Lagrange;,34
12. Direct; , Products; , and; , Finitely ; , Generated; , Abelian; , Groups37
13. Plane; , Isometries; , 42
III. Homomorphisms ; , and; , Factor; , Groups
14. Homomorphisms 44
15. Factor; , Groups 49
16. Factor-Group;, Computations ; , and;, Simple;, Groups 53
17. Group; , Action; , on; , a; , Set; , 58
18. Applications;,of;,G-Sets;,to;,Counting 61
IV. Rings; , and; , Fields
19. Rings;,and;,Fields;, 63
20. Integral;,Domains; , 68
21. Fermat’s; , and; , Euler’s; , Theorems;,72
22. The;, Field;, of;, Quotients;, of;, an;,Integral;, Domain 74
23. Rings;, of;, Polynomials;, 76
24. Factorization;,of;,Polynomials;,over;,a;,Field 79
25. Noncommutative ;,Examples;,85
26. Ordered;, Rings; , and; , Fields;,87
V. Ideals; , and; , Factor; , Rings
27. Homomorphisms ;,and;,Factor;,Rings89
,28. Prime; , and; , Maximal; , Ideals 94
29. Gröb ner ;,Bases;,for;,Ideals; , 99
, VI. Extension; , Fields
30. Introduction;,to;,Extension;,Fields103
31. Vector; , Spaces; , ; , 107
32. Algebraic;, Extensions; , 111
33. Geometric;, Constructions; , 115
34. Finite; , Fields; , 116
VII. Advanced; , Group; , Theory
35. Isomorphism;,Theorems; , 117
36. Series;,of;, Groups; , ; , 119
37. Sylow; , Theorems; , 122
38. Applications; , of; , the;, Sylow;, Theory 124
39. Free; , Abelian; , Groups; , 128
40. Free;, Groups; , ; , 130
41. Group; , Presentations; , 133
VIII. Groups; , in; , Topology
42. Simplicial; , Complexes; , and; , Homology ; , Groups 136
43. Computations ;, of; , Homology ;, Groups 138
44. More;, Homology ;, Computations ;, and;, Applications 140
45. Homological;,Algebra;, 144
IX. Factorization
46. Unique;,Factorization;,Domains148
47. Euclidean; , Domains; , 151
48. Gaussian;,Integers;, and;, Multiplicative ;, Norms 154
X. Automorphisms; , ; , and; , ; , Galois; , ; , Theory
49. Automorphisms;,of;,Fields;,159
50. The; , Isomorphism; , Extension; , Theorem 164
51. Splitting; , Fields; , 165
52. Separable;,Extensions 167
53. Totally ;,Inseparable ;,Extensions171
54. Galois; , Theory 173
55. Illustrations;, of;, Galois; , Theory ;,176
56. Cyclotomic;,Extensions; , 183
57. Insolvability;,of;,the;,Quintic;,18
5;,APPENDIX; , ; , Matrix; , ; , Algebra
; , 187
First Course in Abstract
Algebra A
8th Edition by John B. Fraleigh
All Chapters Full Complete
, CONTENTS
1. Sets;, and; , Relations; , ; , 1
I. Groups; , and; , Subgroups
2. Introduction; , and; , Examples; , 4
3. Binary; , Operations; , 7
4. Isomorphic; , Binary; , Structures;, 9
5. Groups 13
6. Subgroups 17
7. Cyclic; , Groups; , 21
8. Generators; , and; , Cayley; , Digraphs 24
II. Permutations,; , Cosets,; , and; , Direct; , Products
9. Groups; , of; , Permutations; , 26
10. Orbits,;,Cycles,;,and;,the;,Alternating;,Group
s;,30
11. Cosets; , and; , the; , Theorem; , of; , Lagrange;,34
12. Direct; , Products; , and; , Finitely ; , Generated; , Abelian; , Groups37
13. Plane; , Isometries; , 42
III. Homomorphisms ; , and; , Factor; , Groups
14. Homomorphisms 44
15. Factor; , Groups 49
16. Factor-Group;, Computations ; , and;, Simple;, Groups 53
17. Group; , Action; , on; , a; , Set; , 58
18. Applications;,of;,G-Sets;,to;,Counting 61
IV. Rings; , and; , Fields
19. Rings;,and;,Fields;, 63
20. Integral;,Domains; , 68
21. Fermat’s; , and; , Euler’s; , Theorems;,72
22. The;, Field;, of;, Quotients;, of;, an;,Integral;, Domain 74
23. Rings;, of;, Polynomials;, 76
24. Factorization;,of;,Polynomials;,over;,a;,Field 79
25. Noncommutative ;,Examples;,85
26. Ordered;, Rings; , and; , Fields;,87
V. Ideals; , and; , Factor; , Rings
27. Homomorphisms ;,and;,Factor;,Rings89
,28. Prime; , and; , Maximal; , Ideals 94
29. Gröb ner ;,Bases;,for;,Ideals; , 99
, VI. Extension; , Fields
30. Introduction;,to;,Extension;,Fields103
31. Vector; , Spaces; , ; , 107
32. Algebraic;, Extensions; , 111
33. Geometric;, Constructions; , 115
34. Finite; , Fields; , 116
VII. Advanced; , Group; , Theory
35. Isomorphism;,Theorems; , 117
36. Series;,of;, Groups; , ; , 119
37. Sylow; , Theorems; , 122
38. Applications; , of; , the;, Sylow;, Theory 124
39. Free; , Abelian; , Groups; , 128
40. Free;, Groups; , ; , 130
41. Group; , Presentations; , 133
VIII. Groups; , in; , Topology
42. Simplicial; , Complexes; , and; , Homology ; , Groups 136
43. Computations ;, of; , Homology ;, Groups 138
44. More;, Homology ;, Computations ;, and;, Applications 140
45. Homological;,Algebra;, 144
IX. Factorization
46. Unique;,Factorization;,Domains148
47. Euclidean; , Domains; , 151
48. Gaussian;,Integers;, and;, Multiplicative ;, Norms 154
X. Automorphisms; , ; , and; , ; , Galois; , ; , Theory
49. Automorphisms;,of;,Fields;,159
50. The; , Isomorphism; , Extension; , Theorem 164
51. Splitting; , Fields; , 165
52. Separable;,Extensions 167
53. Totally ;,Inseparable ;,Extensions171
54. Galois; , Theory 173
55. Illustrations;, of;, Galois; , Theory ;,176
56. Cyclotomic;,Extensions; , 183
57. Insolvability;,of;,the;,Quintic;,18
5;,APPENDIX; , ; , Matrix; , ; , Algebra
; , 187
