Complete Solution Manual First Course in Abstract Algebra A, 8th Edition Questions & Answers with rationales

SOLUTION MANUAL mn




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




2. Introduction and Examples 4 mn mn




3. Binary Operations 7
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4. Isomorphic Binary Structures 9 m n m n




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




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




9. Groups of Permutations 26
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10. Orbits, Cycles, and the Alternating Groups mn mn mn mn mn




30
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 m n m n m n




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




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




IV. Rings and Fields m n m n




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




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




25. Noncommutative Examples 85 mn




26. Ordered Rings and Fields 87
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V. Ideals and Factor Rings m n m n m n




27. Homomorphisms and Factor Rings mn mn mn 89
28. Prime and Maximal Ideals 94
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,29. Gröbner Bases for Ideals
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, VI. Extension Fields m n




30. Introduction to Extension Fields mn mn mn 103
31. Vector Spaces 107m n




32. Algebraic Extensions 111 m n




33. Geometric Constructions 115 mn




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




35. Isomorphism Theorems 117 mn




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




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 m n m n




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




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




IX. Factorization
46. Unique Factorization Domains 148
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47. Euclidean Domains 151 m n




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




49. Automorphisms of Fields 159 mn mn




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




52. Separable Extensions 167 mn




53. Totally Inseparable Extensions 171
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54. Galois Theory 173
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55. Illustrations of Galois Theory 176 mn mn mn




56. Cyclotomic Extensions 183 m
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57. Insolvability of the Quintic 185 mn mn mn




APPENDIX Matrix Algebramn m n mn m n 187


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