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

SOLUTION MANUAL k




First Course in Abstract
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Algebra A 8th Edition byJohn
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B.Fraleigh
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k All Chapters FullComplete
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, CONTENTS
1. Sets and Relations 1
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I. Groups and Subgroups k k




2. Introduction and Examples 4 k k




3. Binary Operations 7 k




4. Isomorphic Binary Structures 9 k k




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




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




9. Groups of Permutations 26 k k




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




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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 k k k




14. Homomorphisms 44
15. Factor Groups 49 k




16. Factor-Group Computations and Simple Groups 53 k k k k




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




IV. Rings and Fields k k




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




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




22. The Field of Quotients of an Integral Domain 74
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23. Rings of Polynomials 76
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24. Factorizationof Polynomialsovera Field 79 k k k k k




25. Noncommutative Examples 85 k




26. Ordered Rings and Fields 87 k k k




V. Ideals and Factor Rings k k k




27. Homomorphisms and Factor Rings 89 k k k




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




30. Introduction to Extension Fields 103 k k k




31. Vector Spaces 107 k




32. Algebraic Extensions 111 k




33. Geometric Constructions 115 k




34. Finite Fields 116 k




VII. Advanced Group Theory k k




35. IsomorphismTheorems 117 k




36. Series of Groups 119
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37. Sylow Theorems 122 k




38. Applications of the Sylow Theory 124 k k k k




39. Free Abelian Groups 128
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40. Free Groups 130
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41. Group Presentations 133k




VIII. Groups in Topology k k




42. Simplicial Complexes and Homology Groups 136 k k k k




43. Computations of Homology Groups 138 k k k




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




IX. Factorization
46. Unique Factorization Domains 148 k k




47. Euclidean Domains 151 k




48. Gaussian Integers and Multiplicative Norms 154 k k k k




X. Automorphisms and Galois Theory k k k




49. Automorphisms of Fields 159 k k




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




52. SeparableExtensions 167 k




53. TotallyInseparable Extensions 171
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54. Galois Theory 173 k




55. Illustrationsof Galois Theory 176 k k k




56. CyclotomicExtensions 183 k




57. Insolvability of the Quintic 185 k k k




APPENDIX Matrix Algebra k k k k 187


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