书目名称 | Real Algebra | 副标题 | A First Course | 编辑 | Manfred Knebusch,Claus Scheiderer | 视频video | | 概述 | Provides a thorough introduction to real algebra, including the real spectrum.Includes a new chapter on recent developments in real algebraic geometry.A unique reference providing many results that ar | 丛书名称 | Universitext | 图书封面 |  | 描述 | 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 .Einführung 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.. | 出版日期 | Textbook 2022 | 关键词 | real algebra; real algebraic geometry; Hilbert‘s 17th problem; spectral space; real spectrum; positivstel | 版次 | 1 | doi | https://doi.org/10.1007/978-3-031-09800-0 | isbn_softcover | 978-3-031-09799-7 | isbn_ebook | 978-3-031-09800-0Series ISSN 0172-5939 Series E-ISSN 2191-6675 | issn_series | 0172-5939 | copyright | Springer Nature Switzerland AG 2022 |
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