Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Bosch, Siegfried (1944-....)
Titre(s) : Algebra [Texte électronique] : from the viewpoint of Galois theory / Siegfried Bosch
Traduction de : Algebra
Publication : Cham : Birkhäuser, copyright 2018
Description matérielle : 1 ressource dématérialisée
Collection : Birkhäuser advanced texts. Basler Lehrbücher
Lien à la collection : Birkhäuser advanced texts. Basler Lerhbücher (Online)
Note(s) : Traduit de la 8e édition révisée en langue allemande. - Notes bibliogr. Index
The material presented here can be divided into two parts. The first, sometimes referred
to as abstract algebra, is concerned with the general theory of algebraic objects
such as groups, rings, and fields, hence, with topics that are also basic for a number
of other domains in mathematics. The second centers around Galois theory and its applications.
Historically, this theory originated from the problem of studying algebraic equations,
a problem that, after various unsuccessful attempts to determine solution formulas
in higher degrees, found its complete clarification through the brilliant ideas of
E. Galois. The study of algebraic equations has served as a motivating terrain for
a large part of abstract algebra, and according to this, algebraic equations are visible
as a guiding thread throughout the book. To underline this point, an introduction
to the history of algebraic equations is included. The entire book is self-contained,
up to a few prerequisites from linear algebra. It covers most topics of current algebra
courses and is enriched by several optional sections that complement the standard
program or, in some cases, provide a first view on nearby areas that are more advanced.
Every chapter begins with an introductory section on "Background and Overview," motivating
the material that follows and discussing its highlights on an informal level. Furthermore,
each section ends with a list of specially adapted exercises, some of them with solution
proposals in the appendix. The present English edition is a translation and critical
revision of the eighth German edition of the Algebra book by the author. The book
appeared for the first time in 1993 and, in later years, was complemented by adding
a variety of related topics. At the same time it was modified and polished to keep
its contents up to date.
La pagination de l'édition imprimée correspondante est de : VIII-367 p.
Sujet(s) : Galois, Théorie de
Algèbre
Indice(s) Dewey :
512.32 (23e éd.) = Théorie de Galois (mathématiques)
Identifiants, prix et caractéristiques : ISBN 3319951769. - ISBN 9783319951768
Identifiant de la notice : ark:/12148/cb45779745w
Notice n° :
FRBNF45779745
(notice reprise d'un réservoir extérieur)
Table des matières : Elementary Group Theory ; Rings and Polynomials ; Algebraic Field Extensions ;
Galois Theory ; More Group Theory ; Applications of Galois Theory ; Transcendental
Field Extensions.
