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

, CONTENTS
1. Sets and Relations
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I. Groups and Subgroups m m




2. Introduction and Examples 4 m m




3. Binary Operations 7 m




4. Isomorphic Binary Structures 9 m m




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




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




9. Groups of Permutations 26 m m




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




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11. Cosets and the Theorem of Lagrange
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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 m m




14. Homomorphisms 44
15. Factor Groups 49 m




16. Factor-Group Computations and Simple Groups m m m m 53
17. Group Action on a Set 58
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18. Applications of G-Sets to Counting 61 m m m m




IV. Rings and Fields m m




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




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




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 m m m m m




25. Noncommutative Examples 85 m




26. Ordered Rings and Fields 87 m m m




V. Ideals and Factor Rings m m m




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




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




32. Algebraic Extensions 111 m




33. Geometric Constructions 115 m




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




35. Isomorphism Theorems 117 m




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




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




44. More Homology Computations and Applications
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45. Homological Algebra 144 m




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




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




49. Automorphisms of Fields 159 m m




50. The Isomorphism Extension Theorem
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51. Splitting Fields 165 m




52. Separable Extensions 167 m




53. Totally Inseparable Extensions
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54. Galois Theory 173 m




55. Illustrations of Galois Theory 176 m m m




56. Cyclotomic Extensions 183 m




57. Insolvability of the Quintic 185 m m m




APPENDIX Matrix Algebra m m m m 187


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