UID:
almahu_9947359992802882
Format:
Online-Ressource (XI, 366 S.)
Edition:
Online-Ausg. 2011 Electronic reproduction; Available via World Wide Web
ISBN:
9783110250084
Series Statement:
De Gruyter Graduate 11
Content:
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. Celine Carstensen, Volkswohlbund Insurance, Dortmund, Germany;Benjamin Fine, Fairfield University, Connecticut, USA; Gerhard Rosenberger, Universität Hamburg, Germany.
Note:
Includes bibliographical references and index
,
16 Separable Field Extensions17 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; Bibliography; Index;.
,
Preface; 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.
Additional Edition:
ISBN 9783110250091
Language:
English
DOI:
10.1515/9783110250091
URL:
http://www.degruyter.com/doi/book/10.1515/9783110250091
URL:
Volltext
(lizenzpflichtig)
Author information:
Fine, Benjamin, 1948-
Author information:
Rosenberger, Gerhard, 1944-
Author information:
Carstensen-Opitz, Celine.
