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

SOLUTION MANUAL ,




FirstCourseinAbstract
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AlgebraA 8th EditionbyJohn
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B.Fraleigh
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, All ChaptersFullComplete
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, CONTENTS
1. Sets and Relations
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I. Groups and Subgroups , ,




2. Introduction and Examples 4 , ,




3. Binary Operations 7 ,




4. Isomorphic Binary Structures 9 , ,




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




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




9. Groups of Permutations 26 , ,




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




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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 , , ,




14. Homomorphisms 44
15. Factor Groups 49 ,




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




17. Group Action on a Set 58
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18. Applicationsof G-Sets to Counting 61 , , , ,




IV. Rings and Fields , ,




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




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




22. The Field of Quotients of an Integral Domain 74
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23. Rings of Polynomials 76
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24. FactorizationofPolynomialsoveraField 79 , , , , ,




25. Noncommutative Examples 85 ,




26. Ordered Rings and Fields 87 , , ,




V. Ideals and Factor Rings , , ,




27. Homomorphisms and Factor Rings , , , 89
28. Primeand Maximal Ideals 94
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,29. Gröbner Bases for Ideals 99
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, VI. Extension Fields ,




30. Introductionto Extension Fields , , , 103
31. Vector Spaces 107 ,




32. Algebraic Extensions 111 ,




33. GeometricConstructions 115 ,




34. Finite Fields 116 ,




VII. Advanced Group Theory , ,




35. IsomorphismTheorems 117 ,




36. Series of Groups 119 , ,




37. Sylow Theorems 122 ,




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




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




VIII. Groups in Topology , ,




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




43. Computations of Homology Groups 138 , , ,




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




IX. Factorization
46. Unique Factorization Domains 148 , ,




47. Euclidean Domains 151 ,




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




X. Automorphisms and Galois Theory , , ,




49. Automorphisms of Fields 159 , ,




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




52. SeparableExtensions 167 ,




53. TotallyInseparableExtensions 171 , ,




54. Galois Theory 173 ,




55. IllustrationsofGaloisTheory 176 , , ,




56. CyclotomicExtensions 183 ,




57. Insolvability of the Quintic 185 , , ,




APPENDIX Matrix Algebra , , , , 187


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