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Real algebra = a first course /

Knebusch, Manfred.

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Real algebra = a first course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Real algebra/ by Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger.
其他題名:	a first course /
作者:	Knebusch, Manfred.
其他作者:	Scheiderer, Claus.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xii, 206 p. :ill., digital ;24 cm.
內容註:	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
標題:	Algebra. -
電子資源:	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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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 2 4 $a Algebraic Geometry. $3 893861
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