SOLUTION MANUAL First Course in Abstract Algebra A 8th

SOLUTION MANUAL kkkh




First Course in Abstract Algebra
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A
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kkkh 8th Edition by John B. Fraleigh
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kkkh k k k h All Chapters Full Complete
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,
, CONTENTS
1. Sets kkkh and kkkh Relations 1

I. Groups k k k h and k k k h Subgroups

2. Introduction k k k h and k k k h Examples 4
3. Binary k k k h Operations 7
4. Isomorphic k k k h Binary k k k h Structures 9
5. Groups 13
6. Subgroups 17
7. Cyclic kkkh k k k h Groups 21
8. Generators k k k h and k k k h Cayley k k k h Digraphs 24

II. Permutations, Cosets, and Direct Products
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9. Groups kkkh of kkkhPermutations 26
10. Orbits, kkkhCycles, kkkhand kkkhthe kkkhAlternating
kkkhGroups 30
11. Cosets kkkh and kkkhthe kkkhTheorem kkkh of kkkhLagrange 34
12. Direct k k k h Products k k k h and k k k h Finitely k k k h Generated k k k h Abelian k k k h Groups 37
13. Plane k k k h Isometries 42

III. Homomorphisms kkkh and kkkh Factor kkkh Groups

14. Homomorphisms 44
15. Factor k k k h Groups 49
16. Factor-Group k k k h Computations k k k h and k k k h Simple k k k h Groups 53
17. Group kkkhAction kkkhon kkkha kkkhSet 58
18. Applications kkkhof kkkhG-Sets kkkhto kkkhCounting 61

IV. Rings kkkh and kkkh Fields

19. Rings kkkhand kkkhFields 63
20. Integral k k k h Domains 68
21. Fermat’s k k k h and k k k h Euler’s k k k h Theorems 72
22. The k k k h Field k k k h of k k k h Quotients k k k h of k k k h an k k k h Integral k k k h Domain 74
23. Rings k k k h of k k k h Polynomials 76
24. Factorization kkkhof kkkhPolynomials kkkhover kkkha kkkhField 79
25. Noncommutative kkkhExamples 85
26. Ordered k k k h Rings k k k h and k k k h Fields 87

V. Ideals kkkh and kkkh Factor kkkh Rings

27. Homomorphisms kkkhand kkkhFactor kkkhRings 89
28. Prime kkkhand kkkhMaximal kkkhIdeals 94

, 29. Gröbner kkkhBases kkkhfor kkkhIdeals 99