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## Details

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:

## Reviews

*Editorial reviews*

Publisher Synopsis

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 using this book. ... Out of all the books I used in undergrad, this one was one of my favorites because it was easy to use for reference and for independent learning. ... Great foundation establishing book to start building in the domain of Abstract Algebra." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014) "Algebra II: Fields with Structure, Algebras and Advanced Topics is ... a complete algebra course, including both undergraduate and graduate topics. ... The second volume focuses on fields with structure and algebras. ... the choice of topics and their organization are excellent and provide a unifying view of most of algebra. In all, Lorenz's book is a wonderful reference for both teachers and researches, and can be used with much profit for independent study by hard-working students." (Luiz Hendrique de Figueiredo, MathDL, July, 2008) "The author has managed to cover such an amazing wealth of advanced material in a very adroit manner, thereby keeping the representation utmost lively, comprehensible, thorough, always straight to the point, essentially self-contained, methodologically elegant and - all in all - admirably reader-friendly. ... No doubt, this is an outstanding textbook on advanced topics in abstract algebra, mainly in its field-theoretic and number-theoretic aspects, and its availability in English makes it a unique and utmost valuable enrichment of the international textbook literature on the subject." (Werner Kleinert, Zentralblatt MATH, Vol. 1130 (8), 2008) Read more...

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