First Course in Abstract Algebra A
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Il! Il! 8th Edition by JohnB. Fraleigh
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I l ! All Chapters Full Complete
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, CONTENTS
1. Sets and Relations
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I. Groups and Subgroups I l ! I l !
2. Introduction and Examples 4 Il! Il!
3. Binary Operations 7I l !
4. Isomorphic Binary Structures 9 Il ! Il !
5. Groups 13
6. Subgroups 17
7. Cyclic Groups 21
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8. Generators and Cayley Digraphs 24 Il ! Il! Il !
II. Permutations, Cosets, and Direct Products Il! Il! Il! Il!
9. Groups of Permutations 26 Il ! Il!
10. Orbits, Cycles, and the Alternating Groups Il! Il! Il! Il! Il!
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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 l ! I l! I l!
14. Homomorphisms 44
15. Factor Groups 49 Il!
16. Factor-Group Computations and Simple Groups 53 Il! Il ! Il! Il!
17. Group Action on a Set 58
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18. Applications of G-Sets to Counting 61 Il! Il! Il! Il!
IV. Rings and Fields I l ! I l !
19. Rings and Fields 63
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20. Integral Domains 68 Il!
21. Fermat’s and Euler’s Theorems 72Il! Il! Il!
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 Il! Il! Il! Il! Il!
25. Noncommutative Examples 85 Il!
26. Ordered Rings and Fields 87 Il! Il! Il!
V. Ideals and Factor Rings I l ! I l ! I l !
27. Homomorphisms and Factor Rings Il! Il! Il! 89
28. Prime and Maximal Ideals 94
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,29. Gröbner Bases for Ideals
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, VI. Extension Fields I l !
30. Introduction to Extension Fields Il! Il! Il! 103
31. Vector Spaces 107 I l !
32. Algebraic Extensions 111 I l !
33. Geometric Constructions 115 Il!
34. Finite Fields 116
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VII. Advanced Group Theory Il! Il!
35. IsomorphismTheorems 117 Il!
36. Series of Groups 119
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37. Sylow Theorems 122
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38. Applications of the Sylow Theory 124 Il! Il! Il! Il!
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 l ! I l !
42. Simplicial Complexes and Homology Groups 136
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43. Computations of Homology Groups 138 Il! Il! Il!
44. More Homology Computations and Applications 140
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45. Homological Algebra 144 Il!
IX. Factorization
46. Unique Factorization Domains 148
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47. Euclidean Domains 151 I l !
48. Gaussian Integers and Multiplicative Norms 154
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X. Automorphisms and Galois Theory I l ! I l ! I l !
49. Automorphisms of Fields 159 Il! Il!
50. The Isomorphism Extension Theorem 164
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51. Splitting Fields 165 Il!
52. SeparableExtensions 167 Il!
53. Totally Inseparable Extensions
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54. Galois Theory 173 I l !
55. IllustrationsofGalois Theory 176 Il! Il! Il!
56. CyclotomicExtensions 183 Il!
57. Insolvability of the Quintic 185 Il! Il! Il!
APPENDIX Matrix Algebra Il! I l ! Il! I l ! 187
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