Solution Manual for A First Course in Abstract Algebra, 8th Edition by John B. Fraleigh | Complete Solutions for All Chapters | Revised Edition

SOLUTION MANUAL
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First Course in Abstract Alge
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bra A 8th Edition by John B. F
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ll Chapters Full Complete
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, CONTENTS
1. Setsm andm Relations 1

I. Groups and Subgroups m m


II. Permutations, Cosets, and Direct Products
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9. Groupsm ofmPermutations 26
10. Orbits,mCycles,mandmthemAlternatingmGroups
30
11. Cosetsm andmthemTheoremm ofmLagrange 34
12. Directm Productsm andm Finitelym Generatedm Abelianm Groups 37
13. Planem Isometries 42

III. Homomorphisms and Factor Groups m m m




14. Homomorphisms 44
15. Factorm Groups 49
16. Factor-Groupm Computationsm andm Simplem Groups 53
17. GroupmActionmonmamSet 58
18. ApplicationsmofmG-SetsmtomCounting 61

IV. Rings and Fields
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19. RingsmandmFields 63
20. Integralm Domains 68
21. Fermat’sm andm Euler’sm Theorems 72
22. Them Fieldm ofm Quotientsm ofm anm Integralm Domain 74
23. Ringsm ofm Polynomials 76
24. FactorizationmofmPolynomialsmovermamField 79
25. NoncommutativemExamples 85
26. Orderedm Ringsm andm Fields 87

V. Ideals and Factor Rings
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27. HomomorphismsmandmFactormRings 89
28. PrimemandmMaximalmIdeals 94
29. GröbnermBasesmformIdeals 99

, VI. Extension Fields
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30. IntroductionmtomExtensionmFields 103
31. Vectorm Spaces 107
32. Algebraicm Extensions 111
33. GeometricmConstructions 115
34. Finitem Fields 116

VII. Advanced Group Theory
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35. IsomorphismmTheorems 117
36. SeriesmofmGroups 119
37. Sylowm Theorems 122
38. Applicationsm ofm them Sylowm Theory 124
39. Freem Abelianm Groups 128
40. FreemGroups 130
41. Groupm Presentations 133

VIII. Groups in Topology
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42. Simplicialm Complexesm andm Homologym Groups 136
43. Computationsmofm HomologymGroups 138
44. MoremHomologymComputationsmandmApplications 140
45. HomologicalmAlgebra 144

IX. Factorization
46. Uniquem Factorizationm Domains 148
47. Euclideanm Domains 151
48. Gaussianm Integersm andm Multiplicativem Norms 154

X. Automorphisms and Galois Theory
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49. AutomorphismsmofmFields 159
50. Them Isomorphismm Extensionm Theorem 164
51. Splittingm Fields 165
52. SeparablemExtensions 167
53. TotallymInseparablemExtensions171
54. Galoism Theory 173
55. IllustrationsmofmGaloismTheory176
56. CyclotomicmExtensions 183
57. Insolvabilitym ofm them Quintic 185

APPENDIXmm Matrixmm Algebra 187


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