Carstensen-Opitz, Celine
[Author];
Fine, Benjamin
[Author];
Moldenhauer, Anja
[Author];
Rosenberger, Gerhard
[Author]
;
Walter de Gruyter GmbH & Co. KG
Abstract algebra
: applications to galois theory, algebraic geometry, representation theory and cryptography
- [2nd edition]
Description:
Frontmatter -- Preface -- Preface to the second edition -- Contents -- 1. Groups, rings and fields -- 2. Maximal and prime ideals -- 3. Prime elements and unique factorization domains -- 4. Polynomials and polynomial rings -- 5. Field extensions -- 6. Field extensions and compass and straightedge constructions -- 7. Kronecker’s theorem and algebraic closures -- 8. Splitting fields and normal extensions -- 9. Groups, subgroups, and examples -- 10. Normal subgroups, factor groups, and direct products -- 11. Symmetric and alternating groups -- 12. Solvable groups -- 13. Groups actions and the Sylow theorems -- 14. Free groups and group presentations -- 15. Finite Galois extensions -- 16. Separable field extensions -- 17. Applications of Galois theory -- 18. The theory of modules -- 19. Finitely generated Abelian groups -- 20. Integral and transcendental extensions -- 21. The Hilbert basis theorem and the nullstellensatz -- 22. Algebras and group representations -- 23. Algebraic cryptography -- Bibliography -- Index