Solution Manual for A First Course in Abstract Algebra (Latest Edition) by John B. Fraleigh – Complete Solutions to All Chapters

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All ChaptersFullComplete
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, CONTENTS
1. Sets and Relations 1
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I. Groups and Subgroups

2. Introduction and Examples 4 g g g


3. Binary Operations 7 g


4. Isomorphic Binary Structures 9 g


5. Groups 13
6. Subgroups 17
7. Cyclic Groups 21 g


8. Generators and Cayley Digraphs 24 gg g gg g




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




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


30
11. Cosets and the Theorem of Lagrange
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12. Direct Products and Finitely Generated Abelian Groups 37
13. Plane Isometries 42
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III. Homomorphisms and Factor Groups

14. Homomorphisms 44
15. Factor Groups 49
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16. Factor-Group Computations and Simple Groups
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17. Group Action on a Set 58
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18. Applications of G-Sets to Counting 61 g g g g




IV. Rings and Fields

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


21. Fermat’s and Euler’s Theorems
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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 g g g g g


25. Noncommutative Examples 85 g


26. Ordered Rings and Fields g g 87 g g g g




V. Ideals and Factor Rings

27. Homomorphisms and Factor Rings g g g g 89
28. Prime and Maximal Ideals 94
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,29. Gröbne r Bases for Ideals 99
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, VI. Extension Fields

30. Introduction to Extension Fields 103 g g g gg


31. Vector Spaces 107 g


32. Algebraic Extensions 111 gg


33. Geometric Constructions 115 g


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




35. Isomorphism Theorems 117 g


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

42. Simplicial Complexes and Homology Groups
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43. Computations of Homology Groups 138 g g g g


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




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


48. Gaussian Integers and Multiplicative Norms
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X. Automorphisms and Galois Theory
49. Automorphisms of Fields 159 g g


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


52. Separable Extensions 167 g


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


56. CyclotomicExtensions 183
57. Insolvability of the Quintic 185 g g g g g




APPENDIX Matrix Algebra 187


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