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Algebra

Einführung in die Galoistheorie
Language: German
Published/Copyright: 2013
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De Gruyter Studium
This book is in the series
De Gruyter Studium

About this book

The expanded and revised new edition of this text offers an elegant and coherent introduction to the material covered in a university-level algebra course. The solving of systems of equations is a central and unifying approach in the work. The textbook presents the interconnections between group theory, ring theory, and algebraic field theory, and reference to practical applications help to further understanding.

A classic textbook on algebra, now in a revised and expanded edition

Illustrates how the material can be applied, thus contributing to the reader's understanding

Author / Editor information

Gernot Stroth, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale).

Supplementary Materials

Topics

  • Publicly Available

    Frontmatter

    i
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    Vorwort zur 2. Auflage

    vii
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    Vorwort zur 1. Auflage

    viii
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  • Publicly Available

    Inhalt

    xiii
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    1 Ringe

    1
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    2 Körpererweiterungen

    35
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    3 Algebraische Erweiterungen

    40
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    4 Konstruktionen mit Zirkel und Lineal

    55
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    5 Gruppen

    61
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    6 Galoistheorie

    92
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    7 Normale Erweiterungen

    110
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    8 Separable Erweiterungen

    117
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    9 Rein inseparable Erweiterungen

    125
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    10 Radikalerweiterungen

    129
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    11 Regelmäßige n-Ecke

    137
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    12 Kreisteilungskörper

    148
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    13 Norm und Spur

    169
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    14 Abelsche Erweiterungen von ℚ

    175
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    15 Bewertungen und p-adische Zahlen

    179
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    16 Der größte gemeinsame Teiler

    217
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    17 Faktorisierung von Polynomen

    228
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    18 Galoisgruppen

    245
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    19 Angeordnete Körper

    279
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    20 Der Satz von Sturm

    291
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    A Der Körper der komplexen Zahlen

    297
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    B Transzendenz von e und π

    301
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    C Triangulierung von Quadraten

    306
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    Literaturverzeichnis

    311
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    Stichwortverzeichnis

    313
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    Backmatter

    318
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
August 29, 2013
eBook ISBN:
9783110290714
Hardcover published on:
August 19, 2013
Hardcover ISBN:
9783110290707
Pages and Images/Illustrations in book
Front matter:
14
Main content:
317
Illustrations:
20
Tables:
2
https://doi.org/10.1515/9783110290714
eBook ISBN: 9783110290714
Hardcover ISBN: 9783110290707
Keywords for this book
Algebra; Galoistheorie; Polynomgleichung; Gruppentheorie; Körpertheorie; Ringtheorie; Gruppe; Körper; Ring; endlicher Körper; Kreisteilungskörper; Polynom; p-adische Zahl
Audience(s) for this book
Students of mathematics and physics; academic libraries
Safety & product resources
Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
Downloaded on 26.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/9783110290714/html?lang=en
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