Contemporary abstract algebra
Gallian, Joseph A.
Contemporary abstract algebra / Joseph A. Gallian - 10th ed. - US: CRC Press, 2021 - 635 p.
1. Preliminaries
2. Introduction to groups
3. Groups
4. Finite groups: subgroups
5. Cyclic groups
6. Permutation groups
7. Isomorphisms
8. Cosets and lagrange’s theorem
9. External direct products
10. Normal subgroups and factor groups
11. Group homomorphisms
12. Fundamental theorem of finite abelian groups
13. Introduction to rings
14. Integral domains
15. Ideals and factor rings
16. Ring homomorphism
17. Polynomial rings
18. Factorization of polynomials
19. Divisibility in integral domains
20. Extension fields
21. Algebraic extensions
22. Finite fields
23. Geometric constructions
24. Sylow theorems
25. Finite simple groups
26. Generators and relations
27. Symmetry groups
28. Symmetry and counting
29. Cayley digraphs of groups
30. Introduction to algebraic coding theory
31. An introduction to Galois theory
32. Cyclotomic extensions
9780367651787 (hbk)
Algebra, Abstract
512.02 / G1367
Contemporary abstract algebra / Joseph A. Gallian - 10th ed. - US: CRC Press, 2021 - 635 p.
1. Preliminaries
2. Introduction to groups
3. Groups
4. Finite groups: subgroups
5. Cyclic groups
6. Permutation groups
7. Isomorphisms
8. Cosets and lagrange’s theorem
9. External direct products
10. Normal subgroups and factor groups
11. Group homomorphisms
12. Fundamental theorem of finite abelian groups
13. Introduction to rings
14. Integral domains
15. Ideals and factor rings
16. Ring homomorphism
17. Polynomial rings
18. Factorization of polynomials
19. Divisibility in integral domains
20. Extension fields
21. Algebraic extensions
22. Finite fields
23. Geometric constructions
24. Sylow theorems
25. Finite simple groups
26. Generators and relations
27. Symmetry groups
28. Symmetry and counting
29. Cayley digraphs of groups
30. Introduction to algebraic coding theory
31. An introduction to Galois theory
32. Cyclotomic extensions
9780367651787 (hbk)
Algebra, Abstract
512.02 / G1367
