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

SOLUTION MANUAL IIll




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

2. Introduction and Examples 4 IIll IIll



3. Binary Operations 7
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4. Isomorphic Binary Structures I Il l I Il l 9
5. Groups 13
6. Subgroups 17
7. Cyclic Groups 21
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8. Generators and Cayley Digraphs IIll IIll IIll 24

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




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



30
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 I I l l II l l II ll




14. Homomorphisms 44
15. Factor Groups 49 IIll



16. Factor-Group Computations and Simple Groups 53 IIll I Il l IIll IIll



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




IV. Rings I I l l and I I l l Fields

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



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



22. The Field of Quotients of an Integral Domain
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23. Rings of Polynomials 76
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24. Factorization of Polynomials over a Field 79 IIl IIl IIl IIll IIll



25. Noncommutative Examples 85 IIll



26. Ordered Rings and Fields 87 IIll IIll IIll




V. Ideals and Factor I I l l I I l l I I l l Rings

27. Homomorphisms and Factor Rings 89 IIll IIll IIll



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

30. Introduction to Extension Fields 103 IIll IIll IIll



31. Vector Spaces 107 I I l l



32. Algebraic Extensions 111 I I l l



33. Geometric Constructions 115 IIl



34. Finite Fields 116 IIll




VII. Advanced Group Theory IIll IIll




35. Isomorphism Theorems 117 Il



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



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



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 I I l l in I I l l Topology

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



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




IX. Factorization
46. Unique Factorization Domains IIll148 IIll



47. Euclidean Domains 151 I I l l



48. Gaussian Integers and Multiplicative Norms
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X. Automorphisms I I l l and I I l l Galois I I l l Theory
49. Automorphisms of Fields 159 IIll IIll



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



52. Separable Extensions 167 IIl



53. Totally Inseparable Extensions 171
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54. Galois Theory 173 I I l l



55. Illustrations of Galois Theory 176 Il IIl IIl



56. CyclotomicExtensions 183 Il



57. Insolvability of the Quintic 185 IIll IIll IIll




APPENDIX IIll I I l l Matrix IIll I I l l Algebra 187


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