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Real algebraa first course /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Real algebraby 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.
Contained By:	Springer Nature eBook
Subject:	Algebra.
Online resource:	https://doi.org/10.1007/978-3-031-09800-0
ISBN:	9783031098000$q(electronic bk.)

Real algebraa 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$q(electronic bk.)

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

188312
Algebra.

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

Dewey Class. No.: 512.9

Real algebraa first course /
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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.
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650 1 4 $a Order, Lattices, Ordered Algebraic Structures. $3 275673
650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Algebraic Geometry. $3 274807
700 1 $a Scheiderer, Claus. $3 937324
700 1 $a Unger, Thomas, $e contributor. $3 937325
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950 $a Mathematics and Statistics (SpringerNature-11649)