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Titlebook: Real Algebra; A First Course Manfred Knebusch,Claus Scheiderer Textbook 2022 Springer Nature Switzerland AG 2022 real algebra.real algebrai

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发表于 2025-3-21 20:07:54 | 显示全部楼层 |阅读模式
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Titlebook: Real Algebra; A First Course Manfred Knebusch,Claus Scheiderer Textbook 2022 Springer Nature Switzerland AG 2022 real algebra.real algebrai
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
doihttps://doi.org/10.1007/978-3-031-09800-0
isbn_softcover978-3-031-09799-7
isbn_ebook978-3-031-09800-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Nature Switzerland AG 2022
The information of publication is updating

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发表于 2025-3-21 23:49:27 | 显示全部楼层
Ordered Fields and Their Real Closures,eir foundational 1927 paper, it was successfully used by Artin in his solution of Hilbert’s 17th Problem in the same year. Real closed fields are introduced and it is shown that they have the same algebraic properties as the field of real numbers. Moreover the existence and uniqueness of a real clos
发表于 2025-3-22 00:31:00 | 显示全部楼层
Convex Valuation Rings and Real Places,n maps, valuation rings, and places. Valuations are naturally associated with orderings, since every convex subring of an ordered field is a valuation ring. The precise relationship between the orderings of a field that are compatible with a valuation ring, and the orderings of the residue field of
发表于 2025-3-22 07:51:55 | 显示全部楼层
The Real Spectrum,t of the time the aim is to be as general as possible and consider arbitrary commutative rings. However, special features arise in the “geometric setting” where coordinate rings of affine varieties over real closed base fields are considered. Many similarities are exhibited by the real spectrum and
发表于 2025-3-22 11:46:30 | 显示全部楼层
Convex Valuation Rings and Real Places,the latter, is exhibited by the Baer–Krull Theorem. Finally, the Artin–Lang Theorem is presented in the form of a Stellensatz. Other than the Artin–Schreier concept of orderings and real closures, this is the essential input for the solution of Hilbert’s 17th Problem, presented at the end of the chapter.
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发表于 2025-3-22 19:49:22 | 显示全部楼层
发表于 2025-3-22 22:38:08 | 显示全部楼层
Ordered Fields and Their Real Closures,vester and Hermite. Parallel to these two subjects an introduction to the basic notions of quadratic forms over fields and their algebraic theory are given. Applications of these are presented in Chaps. . and ..
发表于 2025-3-23 04:08:33 | 显示全部楼层
Textbook 2022s 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..
发表于 2025-3-23 08:04:03 | 显示全部楼层
0172-5939 med 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..978-3-031-09799-7978-3-031-09800-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
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