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 ll




First Course in Abstract Algebra A
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ll ll 8th Edition by John B. Fraleigh
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ll All Chapters Full Complete
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, CONTENTS
1. Sets l l and l lRelations 1

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

II. Permutations, Cosets, and Direct Products
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9. Groups l l of llPermutations 26
10. Orbits, llCycles, lland llthe llAlternating llGroups
30
11. Cosets ll and llthe llTheorem ll of llLagrange 34
12. Direct l l Products l l and l l Finitely l l Generated l l Abelian l l Groups 37
13. Plane l l Isometries 42

III. Homomorphisms and Factor Groups ll ll ll




14. Homomorphisms 44
15. Factor l l Groups 49
16. Factor-Group l l Computations l l and l l Simple l l Groups 53
17. Group llAction llon lla llSet 58
18. Applications llof llG-Sets llto llCounting 61

IV. Rings and Fields ll ll




19. Rings lland llFields 63
20. Integral l l Domains 68
21. Fermat’s l l and l l Euler’s l l Theorems 72
22. The l l Field l l of l l Quotients l l of l l an l l Integral l l Domain 74
23. Rings l l of l l Polynomials 76
24. Factorization llof llPolynomials lover lla llField 79
25. Noncommutative llExamples 85
26. Ordered l l Rings l l and l l Fields 87

V. Ideals and Factor Rings
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27. Homomorphisms lland llFactor llRings 89
28. Prime lland llMaximal llIdeals 94

,29. Gröbner llBases llfor llIdeals 99

, VI. Extension l l Fields

30. Introduction llto llExtension llFields 103
31. Vector l l Spaces 107
32. Algebraic l l Extensions 111
33. Geometric lConstructions 115
34. Finite ll Fields 116

VII. Advanced Group Theory
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35. Isomorphism lTheorems 117
36. Series llof llGroups 119
37. Sylow l l Theorems 122
38. Applications l l of l l the l l Sylow l l Theory 124
39. Free l l Abelian l l Groups 128
40. Free llGroups 130
41. Group l l Presentations 133

VIII. Groups in Topology l l l l




42. Simplicial l l Complexes l l and l l Homology l l Groups 136
43. Computations llof l lHomology llGroups 138
44. More llHomology llComputations lland llApplications 140
45. Homological llAlgebra 144

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

X. Automorphisms l l and l l Galois l l Theory
49. Automorphisms llof llFields 159
50. The l l Isomorphism l l Extension l l Theorem 164
51. Splitting ll Fields 165
52. Separable lExtensions 167
53. Totally llInseparable llExtensions 171
54. Galois l l Theory 173
55. Illustrations lof lGalois lTheory 176
56. CyclotomiclExtensions 183
57. Insolvability l l of l l the l l Quintic 185

APPENDIX ll l l Matrix ll ll Algebra 187


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