Solution Manual First Course in Abstract Algebra A, 8th Edition by John B. Fraleigh All 1-56 Chapters Covered ,Latest Edition,ISBN:,9780136731627

SOLUTION MANUAL ii




First Course in Abstract Algebra A
ii ii ii ii ii ii




ii ii 8th Edition by John B. Fraleigh
ii ii ii i ii ii ii




ii All Chapters Full Complete
ii ii ii

, CONTENTS
1. Sets i i and i iRelations 1

I. Groups and Subgroups
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2. Introduction i i and i i Examples 4
3. Binary i i Operations 7
4. Isomorphic i i Binary i i Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic ii i i Groups 21
8. Generators i i and i i Cayley i i Digraphs 24

II. Permutations, Cosets, and Direct Products
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9. Groups i i of iiPermutations 26
10. Orbits, iiCycles, iiand iithe iiAlternating iiGroups
30
11. Cosets ii and iithe iiTheorem ii of iiLagrange 34
12. Direct i i Products i i and i i Finitely i i Generated i i Abelian i i Groups 37
13. Plane i i Isometries 42

III. Homomorphisms and Factor Groups ii ii ii




14. Homomorphisms 44
15. Factor i i Groups 49
16. Factor-Group i i Computations i i and i i Simple i i Groups 53
17. Group iiAction iion iia iiSet 58
18. Applications iiof iiG-Sets iito iiCounting 61

IV. Rings and Fields ii ii




19. Rings iiand iiFields 63
20. Integral i i Domains 68
21. Fermat’s i i and i i Euler’s i i Theorems 72
22. The i i Field i i of i i Quotients i i of i i an i i Integral i i Domain 74
23. Rings i i of i i Polynomials 76
24. Factorization iiof iiPolynomials iover iia iiField 79
25. Noncommutative iiExamples 85
26. Ordered i i Rings i i and i i Fields 87

V. Ideals and Factor Rings
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27. Homomorphisms iiand iiFactor iiRings 89
28. Prime iiand iiMaximal iiIdeals 94

,29. Gröbner iiBases iifor iiIdeals 99

, VI. Extension i i Fields

30. Introduction iito iiExtension iiFields 103
31. Vector i i Spaces 107
32. Algebraic i i Extensions 111
33. Geometric iConstructions 115
34. Finite ii Fields 116

VII. Advanced Group Theory
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35. Isomorphism iTheorems 117
36. Series iiof iiGroups 119
37. Sylow i i Theorems 122
38. Applications i i of i i the i i Sylow i i Theory 124
39. Free i i Abelian i i Groups 128
40. Free iiGroups 130
41. Group i i Presentations 133

VIII. Groups in Topology i i i i




42. Simplicial i i Complexes i i and i i Homology i i Groups 136
43. Computations iiof i iHomology iiGroups 138
44. More iiHomology iiComputations iiand iiApplications 140
45. Homological iiAlgebra 144

IX. Factorization
46. Unique i i Factorization i i Domains 148
47. Euclidean i i Domains 151
48. Gaussian i i Integers i i and i i Multiplicative i i Norms 154

X. Automorphisms i i and i i Galois i i Theory
49. Automorphisms iiof iiFields 159
50. The i i Isomorphism i i Extension i i Theorem 164
51. Splitting ii Fields 165
52. Separable iExtensions 167
53. Totally iiInseparable iiExtensions 171
54. Galois i i Theory 173
55. Illustrations iof iGalois iTheory 176
56. CyclotomiciExtensions 183
57. Insolvability i i of i i the i i Quintic 185

APPENDIX ii i i Matrix ii ii Algebra 187


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