Solution Manual for First Course in Abstract Algebra A 8th Edition

SOLUTION MANUAL b




First Course in Abstract
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Algebra A 8th Edition by John
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B. Fraleigh
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b All Chapters Full Complete
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, CONTENTS
1. Sets and Relations 1
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I. Groups and Subgroups
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2. Introduction and Examples 4 b b



3. Binary Operations 7b



4. Isomorphic Binary Structures 9 b b



5. Groups 13
6. Subgroups 17
7. Cyclic Groups 21
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8. Generators and Cayley Digraphs 24 b b b




II. Permutations, Cosets, and Direct Products b b b b




9. Groups of Permutations 26b b



10. Orbits, Cycles, and the Alternating Groups b b b b b



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11. Cosets and the Theorem of Lagrange 34
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12. Direct Products and Finitely Generated Abelian Groups 37
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13. Plane Isometries 42
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III. Homomorphisms and Factor Groups b b b




14. Homomorphisms 44
15. Factor Groups 49
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16. Factor-Group Computations and Simple Groups 53 b b b b



17. Group Action on a Set 58
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18. Applications of G-Sets to Counting 61 b b b b




IV. Rings and Fieldsb b




19. Rings and Fields 63
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20. Integral Domains 68 b



21. Fermat’s and Euler’s Theorems 72 b b b



22. The Field of Quotients of an Integral Domain
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23. Rings of Polynomials 76
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24. Factorization of Polynomials over a Field 79 b b b b b



25. Noncommutative Examples 85 b



26. Ordered Rings and Fields 87 b b b




V. Ideals and Factor Rings
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27. Homomorphisms and Factor Rings 89 b b b



28. Prime and Maximal Ideals 94
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,29. Gröbner Bases for Ideals 99
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, VI. Extension Fields b




30. Introduction to Extension Fields 103 b b b



31. Vector Spaces 107 b



32. Algebraic Extensions 111 b



33. Geometric Constructions 115 b



34. Finite Fields 116
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VII. Advanced Group Theory b b




35. Isomorphism Theorems 117 b



36. Series of Groups 119
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37. Sylow Theorems 122
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38. Applications of the Sylow Theory 124 b b b b



39. Free Abelian Groups 128
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40. Free Groups 130
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41. Group Presentations 133
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VIII. Groups in Topology b b




42. Simplicial Complexes and Homology Groups 136
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43. Computations of Homology Groups 138 b b b



44. More Homology Computations and Applications 140
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45. Homological Algebra 144 b




IX. Factorization
46. Unique Factorization Domains 148
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47. Euclidean Domains 151 b



48. Gaussian Integers and Multiplicative Norms 154
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X. Automorphisms and Galois Theory b b b




49. Automorphisms of Fields 159 b b



50. The Isomorphism Extension Theorem164
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51. Splitting Fields 165 b



52. Separable Extensions 167 b



53. Totally Inseparable Extensions 171
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54. Galois Theory 173 b



55. Illustrations of Galois Theory 176 b b b



56. CyclotomicExtensions 183 b



57. Insolvability of the Quintic 185 b b b




APPENDIX Matrix Algebra b b b b 187


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