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Algebra

Verfasser/in: Falko Lorenz; Silvio Levy
Verlag: New York : Springer, 2006-2008.
Serien: Universitext.
Ausgabe/Format   E-Book : Dokument : EnglischAlle Ausgaben und Formate anzeigen
Datenbank:WorldCat
Zusammenfassung:
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  Weiterlesen…
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Gattung/Form: Textbooks
Manuels d'enseignement supérieur
Physisches Format Print version:
Lorenz, Falko.
Algebra.
New York : Springer, 2006-2008
(DLC) 2005932557
(OCoLC)63127532
Medientyp: Dokument, Internetquelle
Dokumenttyp: Internet-Ressource, Computer-Datei
Alle Autoren: Falko Lorenz; Silvio Levy
ISBN: 9780387316086 0387316086 9780387724881 0387724885
OCLC-Nummer: 209914197
Anmerkungen: Textbook for graduates.
Beschreibung: 1 online resource (2 v.(vi, 293; ix, 336) : ill.
Inhalt: 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.
Serientitel: Universitext.
Andere Titel Einführung in die Algebra.
Verfasserangabe: Falko Lorenz.
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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  Weiterlesen…

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