Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics by Falko Lorenz

Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics

byFalko LorenzTranslated bySilvio Levy

Paperback | December 27, 2007

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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 it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What's more, the book contains some lesser known or nontraditional results - for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.

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Title:Algebra: Volume II: Fields with Structure, Algebras and Advanced TopicsFormat:PaperbackDimensions:350 pages, 9.25 × 6.1 × 0.03 inPublished:December 27, 2007Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387724877

ISBN - 13:9780387724874

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Table of Contents

Foreword.- 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.- Index.

Editorial Reviews

From the reviews:"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)