Abstract algebra / Dan Saracino.
By: Saracino, Dan.
London, United Kingdom : Published by ED-Tech Press, ©2022Edition: Second, Global edition.Description: 313 pages ; 23 cm.ISBN: 9781804060032 .Subject(s): Abstract algebraDDC classification: 512.02 Sa71Item type | Current location | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
Books | College Library General Circulation Section | GC | GC 512.02 Sa71 2022 (Browse shelf) | Available | HNU004344 |
Includes index.
1. Binary Operations
2. Groups
3. Fundamental Theorems about Groups
4. Powers of an Element; Cyclic Groups
5. Subgroups
6. Direct Products
7. Functions
8. Symmetric Groups
9. Equivalence Relations; Cosets
10. Counting the Elements of a Finite Group
11. Normal Groups
12. Homomorphisms
13. Homomorphisms and Normal Subgroups
14. Direct Products and Finite Abelian Groups
15. Sylow Theorems
16. Rings
17. Subrings, Ideals, and Quotient Rings
18. Ring Homomorphisms
19. Polynomials
20. From Polynomials to Fields
21. Unique Factorization Domains
22. Extension of Fields
23. Constructions with Straightedge and Compass
24. Normal and Separable Extensions
25. Galois Theory
26. Solvability
The presentation of the sections is given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and proof of the Primitive Element of Theorem.
College of Education Bachelor of Secondary Education major in Mathematics
in English
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