Format:
1 Online-ressource (XIII, 407 Seiten)
,
Illustrationen
Edition:
2nd edition
ISBN:
9783110603996
,
9783110605259
Series Statement:
De Gruyter graduate
Content:
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
Note:
Literaturverzeichnis: Seite 399-401
Additional Edition:
ISBN 9783110603934
Additional Edition:
Erscheint auch als Druck-Ausgabe Carstensen-Opitz, Celine Abstract algebra Berlin : De Gruyter, 2019 ISBN 3110603934
Additional Edition:
ISBN 9783110603934
Language:
English
Subjects:
Mathematics
Keywords:
Universelle Algebra
;
Lehrbuch
DOI:
10.1515/9783110603996
URL:
Volltext
(lizenzpflichtig)
Author information:
Rosenberger, Gerhard 1944-
Author information:
Moldenhauer, Anja
Author information:
Fine, Benjamin 1948-