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Algebra

作者: Falko Lorenz; Silvio Levy
出版商: New York : Springer, 2006-2008.
叢書: Universitext.
版本/格式:   電子書 : 文獻 : 英語所有版本和格式的總覽
資料庫:WorldCat
提要:
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  再讀一些...
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類型/形式: Textbooks
Manuels d'enseignement supérieur
其他的實體格式: Print version:
Lorenz, Falko.
Algebra.
New York : Springer, 2006-2008
(DLC) 2005932557
(OCoLC)63127532
資料類型: 文獻, 網際網路資源
文件類型: 網路資源, 電腦資料
所有的作者/貢獻者: Falko Lorenz; Silvio Levy
ISBN: 9780387316086 0387316086 9780387724881 0387724885
OCLC系統控制編碼: 209914197
注意: Textbook for graduates.
描述: 1 online resource (2 v.(vi, 293; ix, 336) : ill.
内容: 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.
叢書名: Universitext.
其他題名: Einführung in die Algebra.
責任: Falko Lorenz.
更多資訊:

摘要:

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  再讀一些...

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