SOLUTION MANUAL First Course in Abstract Algebra A 8th Edition by John B. Fraleigh All Chapters Full Complete

SOLUTION MANUAL w




First Course in Abstract
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wAlgebra A 8th Edition by John
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B. Fraleigh
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w All Chapters Full Complete
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, CONTENTS
1. Sets and Relations 1
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I. Groups and Subgroups w w




2. Introduction and Examples 4 w w




3. Binary Operations 7w




4. Isomorphic Binary Structures 9 w w




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




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




9. Groups of Permutations 26w w




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




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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 w w w




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




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




IV. Rings and Fields w w




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




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




22. The Field of Quotients of an Integral Domain 74
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23. Rings of Polynomials 76
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24. Factorization of Polynomials over a Field 79 w w w w w




25. Noncommutative Examples 85 w




26. Ordered Rings and Fields 87 w w w




V. Ideals and Factor Rings w w w




27. Homomorphisms and Factor Rings 89 w w w




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




30. Introduction to Extension Fields 103 w w w




31. Vector Spaces 107 w




32. Algebraic Extensions 111 w




33. Geometric Constructions 115 w




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




35. Isomorphism Theorems 117 w




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




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 w w




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




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




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




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




49. Automorphisms of Fields 159 w w




50. The Isomorphism Extension Theorem 164
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51. Splitting Fields 165 w




52. Separable Extensions 167 w




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




55. Illustrations of Galois Theory 176 w w w




56. CyclotomicExtensions 183 w




57. Insolvability of the Quintic 185 w w w




APPENDIX Matrix Algebra w w w w 187


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