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＜電子ブック＞
Real Algebra : A First Course / by Manfred Knebusch, Claus Scheiderer
(Universitext. ISSN:21916675)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XII, 206 p. 1 illus : online resource
著者標目	*Knebusch, Manfred author Scheiderer, Claus author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry FREE:Order, Lattices, Ordered Algebraic Structures FREE:Field Theory and Polynomials FREE:Commutative Rings and Algebras FREE:Algebraic Geometry
一般注記	1 Ordered fields and their real closures -- 2 Convex valuation rings and real places -- 3 The real spectrum -- 4 Recent developments 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 inlinear algebra, field theory and ring theory. It also provides a carefully written reference for specialists in real algebra, real algebraic geometry and related fields HTTP:URL=https://doi.org/10.1007/978-3-031-09800-0

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