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Contemporary abstract algebra / Joseph A. Gallian

By: Material type: TextTextPublication details: US: CRC Press, 2021Edition: 10th edDescription: 635 pISBN:
  • 9780367651787 (hbk)
Subject(s): DDC classification:
  • 512.02 G1367
Contents:
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
List(s) this item appears in: Mathematics_Fy2021-22
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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

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