Abstract Algebra
Applications to Galois Theory, Algebraic Geometry and Cryptography
1st Edition
Published on 28. January 2011
Book
Hardback
XI, 366 pages
978-3-11-025008-4 (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; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics.
More details
Series
Language
English
Place of publication
Berlin/Boston
Germany
Target group
College/higher education
US School Grade: From College Freshman to College Senior
Illustrations
Num. figs.
Num. figs.
Dimensions
Height: 240 mm
Width: 170 mm
Weight
646 gr
ISBN-13
978-3-11-025008-4 (9783110250084)
Schweitzer Classification
Other editions
New editions
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
Additional editions
Celine Carstensen | Benjamin Fine | Gerhard Rosenberger
Abstract Algebra
Applications to Galois Theory, Algebraic Geometry and Cryptography
E-Book
02/2011
1st Edition
De Gruyter
€54.95
Available for download
Persons
Celine ?Carstensen, Volkswohlbund Insurance, Dortmund, Germany;Benjamin Fine, Fairfield University, Connecticut, USA; Gerhard Rosenberger, Universität Hamburg, Germany.
Content
? 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 Algebraic Cryptography