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

SOLUTION MANUAL n




FIRST COURSE IN
n n




ABSTRACT ALGEBRA A
n n n n




n n 8TH EDITION BY JOHN B.
n n n n




n FRALEIGH n n




n ALL CHAPTERS FULL
n n




COMPLETE
n

,
, CONTENTS
1. Sets n and n Relations 1


I. Groups and Subgroups
n n




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

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




9. Groups n of nPermutations 26
10. Orbits, nCycles, nand nthe nAlternating
nGroups 30
11. Cosets nand nthe n Theorem n of n Lagrange 34
12. Direct n Products n and n Finitely n Generated n Abelian n Groups 37
13. Plane n Isometries 42


III. Homomorphisms and Factor Groups n n n




14. Homomorphisms 44
15. Factor n Groups 49
16. Factor-Group n Computations n and n Simple n Groups 53
17. Group nAction non na nSet 58
18. Applications nof nG-Sets nto nCounting 61


IV. Rings and Fieldsn n




19. Rings nand nFields 63
20. Integral n Domains 68
21. Fermat’s n and n Euler’s n Theorems 72
22. The n Field n of n Quotients n of n an n Integral n Domain 74
23. Rings n of n Polynomials 76
24. Factorization nof nPolynomials nover na nField 79
25. Noncommutative nExamples 85
26. Ordered n Rings n and n Fields 87


V. Ideals and Factor Rings
n n n




27. Homomorphisms nand nFactor nRings 89

, 28. Prime nand nMaximal nIdeals 94
29. Gröbner nBases nfor nIdeals 99