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Real algebra = a first course /

Knebusch, Manfred.

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Real algebra = a first course /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Real algebra/ by Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger.
Reminder of title:	a first course /
Author:	Knebusch, Manfred.
other author:	Scheiderer, Claus.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xii, 206 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Ordered fields and their real closures -- 2 Convex valuation rings and real places -- 3 The real spectrum -- 4 Recent developments.
Contained By:	Springer Nature eBook
Subject:	Algebra. -
Online resource:	https://doi.org/10.1007/978-3-031-09800-0
ISBN:	9783031098000

Real algebra = a first course /
Knebusch, Manfred.

Real algebraa first course /[electronic resource] :by Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger. - Cham :Springer International Publishing :2022. - xii, 206 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

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 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.

ISBN: 9783031098000

Standard No.: 10.1007/978-3-031-09800-0doiSubjects--Topical Terms:

516203
Algebra.

LC Class. No.: QA152.3 / .K54 2022

Dewey Class. No.: 512.9

Real algebra = a first course /
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100 1 $a Knebusch, Manfred. $3 735191
240 1 0 $a Einfuhrung in die reelle Algebra. $l English
245 1 0 $a Real algebra $h [electronic resource] : $b a first course / $c by Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xii, 206 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $a 1 Ordered fields and their real closures -- 2 Convex valuation rings and real places -- 3 The real spectrum -- 4 Recent developments.
520 $a 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.
650 0 $a Algebra. $3 516203
650 1 4 $a Order, Lattices, Ordered Algebraic Structures. $3 896039
650 2 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Algebraic Geometry. $3 893861
700 1 $a Scheiderer, Claus. $3 3607843
700 1 $a Unger, Thomas, $e contributor. $3 3607844
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-031-09800-0
950 $a Mathematics and Statistics (SpringerNature-11649)