Abstract Algebra
Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
2nd Edition
Published on 2. September 2019
XIV, 407 pages
978-3-11-060399-6 (ISBN)
Description
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.
More details
Series
Edition
2nd rev. and ext. edition
Language
English
Place of publication
Berlin/Boston
Germany
Target group
College/higher education
US School Grade: From College Freshman to College Senior
Edition type
Revised edition
Illustrations
15 Abbildungen, 15 s/w Tabellen
15 ill., 15 tbl.
File size
5,76 MB
ISBN-13
978-3-11-060399-6 (9783110603996)
Schweitzer Classification
Other editions
New editions
Gerhard Rosenberger | Annika Schürenberg | Leonard Wienke
Abstract Algebra
With Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
E-Book
07/2024
3rd Edition
De Gruyter
€69.95
Available for download
E-Book
02/2022
3rd Edition
De Gruyter
€44.95
Available for download
Additional editions
Celine Carstensen-Opitz | Benjamin Fine | Anja Moldenhauer
Abstract Algebra
Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
E-Book
09/2019
2nd Edition
De Gruyter
€64.95
Available for download
Celine Carstensen-Opitz | Benjamin Fine | Anja Moldenhauer
Abstract Algebra
Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
Book
09/2019
2nd Edition
De Gruyter
€64.95
Article exhausted; check for reprint
Persons
Celine
Carstensen-Opitz
, Technical University of Dortmund, Germany;
Benjamin Fine
, Fairfield University, Connecticut, USA;
Gerhard Rosenberger,
University of Hamburg, Germany;
Anja Moldenhauer
, University of Hamburg, Germany.
Content
- Intro
- 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
