A First Course in Abstract Algebra (8th Edition) by John B. Fraleigh – Solution Manual | All Chapters Complete

SOLUTION MANUAL ee




First Course in Abstract Algebra A
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ee ee 8th Edition by John B. Fraleigh
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, CONTENTS


1. Sets and Relations 1
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I. Groups and Subgroups e e e e




2. Introduction and Examples ee ee 4
3. Binary e e Operations 7
4. Isomorphic Binary Structures
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5. Groups 13
6. Subgroups 17
7. Cyclic ee e e Groups 21
8. Generators and Cayley Digraphs ee ee ee 24


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




9. Groups of Permutations26
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10. Orbits, Cycles, and the Alternating
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ee Groups 30
11. Cosets and the Theorem of Lagrange
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12. Direct Products and Finitely Generated Abelian Groups
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13. Plane Isometries 42
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III. Homomorphisms and Factor Groups ee ee ee




14. Homomorphisms 44
15. Factor Groups 49
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16. Factor-Group Computations and Simple Groups 53
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17. Group Action on a Set
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18. Applications of G-Sets to Counting 61
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, IV. Rings and Fields e e e e




19. Rings and Fields 63
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20. Integral Domains 68
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21. Fermat’s and Euler’s Theorems
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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
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25. Noncommutative Examples 85 ee




26. Ordered Rings and Fields
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V. Ideals and Factor Rings
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27. Homomorphisms and Factor Rings 89 ee ee ee




28. Prime and Maximal Ideals
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29. Gröbner Bases for Ideals
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, VI. Extension Fields e e




30. Introduction to Extension Fields ee ee ee 103
31. Vector e e Spaces 107
32. Algebraic Extensions 111 ee




33. Geometric Constructions 115 ee




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




35. Isomorphism Theorems 117 ee




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




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




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




IX. Factorization

46. Unique Factorization Domains
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47. Euclidean Domains 151 ee