Universitext : A First Course - Claus Scheiderer

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Universitext

A First Course

By: Claus Scheiderer, Thomas Unger (Translator), Manfred Knebusch

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Paperback | 23 October 2022

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220 Pages

Dimensions(cm)
15.5 x 23.3 x 1.8

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This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of the classic textbook Einfuehrung in die reelle Algebra. Beginning with the basics of ordered fields and their real closures, the book proceeds to discuss methods for counting the number of real roots of polynomials. Followed by a thorough introduction to Krull valuations, this culminates in Artin's solution of Hilbert's 17th Problem. Next, the fundamental concept of the real spectrum of a commutative ring is introduced with applications. The final chapter gives a brief overview of important developments in real algebra and geometry-as far as they are directly related to the contents of the earlier chapters-since the publication of the original German edition. Real Algebra is aimed at advanced undergraduate and beginning graduate students who have a good grounding in linear algebra, field theory and ring theory. It also provides a carefully written reference for specialists in real algebra, real algebraic geometry and related fields.

Industry Reviews

"More than 30 years after its initial publication, the present textbook is still a very valuable source for results in real algebra. It can serve as a textbook for a university course, but also experts will benefit from the nice account of concepts and results. It's great that the book is available again, in particular in an English translation for an international audience." (Tim Netzer, zbMATH 1505.13001, 2023)

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