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Algebra

Author: Falko Lorenz; Silvio Levy
Publisher: New York : Springer, 2006-2008.
Series: Universitext.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic  Read more...
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Genre/Form: Textbooks
Manuels d'enseignement supérieur
Additional Physical Format: Print version:
Lorenz, Falko.
Algebra.
New York : Springer, 2006-2008
(DLC) 2005932557
(OCoLC)63127532
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Falko Lorenz; Silvio Levy
ISBN: 9780387316086 0387316086 9780387724881 0387724885
OCLC Number: 209914197
Notes: Textbook for graduates.
Description: 1 online resource (2 v.(vi, 293; ix, 336) : ill.
Contents: Vol. I. Fields and Galois theory / with the collaboration of the translator, Silvio Levy --
Constructibility with Ruler and Compass --
Algebraic Extensions --
Simple Extensions --
Fundamentals of Divisibility --
Prime Factorization in Polynomial Rings. Gauss's Theorem --
Polynomial Splitting Fields --
Separable Extensions --
Galois Extensions --
Finite Fields, Cyclic Groups and Roots of Unity --
Group Actions --
Applications of Galois Theory to Cyclotomic Fields --
Further Steps into Galois Theory --
Norm and Trace --
Binomial Equations --
Solvability of Equations --
Integral Ring Extensions --
The Transcendence of [pi] --
Transcendental Field Extensions --
Hilbert's Nullstellensatz --
Appendix: Problems and Remark --
Index of Notation. Vol. 2. Fields with structure, algebras, and advanced topics / with the collaboration of the translator, Silvio Levy --
Ordered Fields and Real Fields --
Hilbert's Seventeenth Problem and the Real Nullstellensatz --
Orders and Quadratic Forms --
Absolute Values on Fields --
Residue Class Degree and Ramification Index --
Local Fields --
Witt Vectors --
The Tsen Rank of a Field --
Fundamentals of Modules --
Wedderburn Theory --
Crossed Products --
The Brauer Group of a Local Field --
Local Class Field Theory --
Semisimple Representations of Finite Groups --
The Schur Group of a Field --
Appendix: Problems and Remarks.
Series Title: Universitext.
Other Titles: Einführung in die Algebra.
Responsibility: Falko Lorenz.
More information:

Abstract:

This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read  Read more...

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From the reviews: "The approach taken by the author is very straightforward, both in its presentation of proofs and its examples. Unlike some books, it is very possible to teach yourself the subject Read more...

 
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