SOLUTION MANUAL for First Course In Abstract Algebra A 8th Edition By John B. Fraleigh All Chapters Full Complete A+

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

, CONTENTS
1. Sets and Relations
is is 1

I. Groups and Subgroups i s i s




2. Introduction and Examples 4 is is



3. Binary Operations 7
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4. Isomorphic Binary Structures 9 i s i s



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




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




9. Groups of Permutations 26 is is



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



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 i s is is




14. Homomorphisms 44
15. Factor Groups 49
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16. Factor-Group Computations and Simple Groups 53 is i s is is



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




IV. Rings and Fields i s i s




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



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 is is is is is



25. Noncommutative Examples 85 is



26. Ordered Rings and Fields 87 is is is




V. Ideals and Factor Rings i s i s i s




27. Homomorphisms and Factor Rings is is is 89
28. Prime and Maximal Ideals
is 94 is is

,29. Gröbner Bases for Ideals
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, VI. Extension Fields i s




30. Introduction to Extension Fields is is is 103
31. Vector Spaces 107 i s



32. Algebraic Extensions 111 i s



33. Geometric Constructions 115 is



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




35. IsomorphismTheorems 117 is



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



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 i s i s




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



44. More Homology Computations and Applications
is 140 is is is



45. Homological Algebra 144 is




IX. Factorization
46. Unique Factorization Domains 148is is



47. Euclidean Domains 151 i s



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




49. Automorphisms of Fields 159 is is



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



52. Separable Extensions 167 is



53. Totally Inseparable Extensions
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54. Galois Theory 173 i s



55. Illustrations of Galois Theory 176 is is is



56. CyclotomicExtensions 183 is



57. Insolvability of the Quintic 185 is is is




APPENDIX Matrix Algebra is i s is i s 187


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