Complete Solution Manual First Course in Abstract Algebra A, 8th Edition Questions & Answers with rationales

First Course in Abstract Algebra 8th Edition Fraleigh Brand Solutions Manual CONTENTS 0. Sets and Relations 01 I. Groups and Subgroups 1. Binary Operations 05 2. Groups 08 3. Abelian Examples 14 4. Nonabelian Examples 19 5. Subgroups 22 6. Cyclic Groups 27 7. Generators and Cayley Digraphs 32 II. Structure of Groups 8. Groups of Permutations 34 9. Finitely Generated Abelian Groups 40 10. Cosets and the Theorem of Lagrange 45 11. Plane Isometries 50 III. Homomorphisms and Factor Groups 12. Factor Groups 53 13. Factor Group Computations and Simple Groups 58 14. Group Action on a Set 65 15. Applications of G-Sets to Counting 70 VI. Advanced Group Theory 16. Isomorphism Theorems 73 17. Sylow Theorems 75 18. Series of Groups 80 19. Free Abelian Groups 85 20. Free Groups 88 21. Group Presentations 91 V. Rings and Fields 22. Rings and Fields 95 23. Integral Domains 102 24. Fermat’s and Euler’s Theorems 106 25. RSA Encryption 109 VI. Constructing Rings and Fields 26. The Field of Quotients of an Integral Domain 110 27. Rings of Polynomials 112 28. Factorization of Polynomials over a Field 116 29. Algebraic Coding Theory 123 30. Homomorphisms and Factor Rings 125 31. Prime and Maximal Ideals 131 32. Noncommutative Examples 137 VII. Commutative Algebra 33. Vector Spaces 140 34. Unique Factorization Domains 145 35. Euclidean Domains 149 36. Number Theory 154 37. Algebraic Geometry 160 38. Gröbner Bases for Ideals 163 VIII. Extension Fields 39. Introduction to Extension Fields 168 40. Algebraic Extensions 174 41. Geometric Constructions 179 42. Finite Fields 182 IX. Galois Theory 43. Automorphisms of Fields 185 44. Splitting Fields 191 45. Separable Extensions 195 46. Galois Theory 199 47. Illustrations of Galois Theory 203 48. Cyclotomic Extensions 211 49. Insolvability of the Quintic 214 APPENDIX: Matrix Algebra 216