Manfred Knebusch: Real Algebra | Taschenbuch

Cover: 9783031097997 | Real Algebra | A First Course | Manfred Knebusch (u. a.) | Taschenbuch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

¿Manfred Knebusch is Professor Emeritus at the University of Regensburg. He has written nine books and more than 80 papers on the algebraic theory of quadratic forms over rings and fields, valuation theory, real algebra and real algebraic geometry. His current research focusses on tropical geometry.

Claus Scheiderer is Professor at Konstanz University. His primary research interests are real algebraic geometry and convex algebraic geometry.

Thomas Unger is Associate Professor at University College Dublin. His research interests include quadratic and hermitian forms, algebras with involution, and noncommutative real algebra and geometry.

Zusammenfassung

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 are hard to find elsewhere

Inhaltsverzeichnis

1 Ordered fields and their real closures.- 2 Convex valuation rings and real places.- 3 The real spectrum.- 4 Recent developments.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xii 206 S. 1 s/w Illustr. 206 p. 1 illus.
ISBN-13:	9783031097997
ISBN-10:	3031097998
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Knebusch, Manfred Scheiderer, Claus
Übersetzung:	Unger, Thomas
Auflage:	1st edition 2022
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG Universitext
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 13 mm
Von/Mit:	Manfred Knebusch (u. a.)
Erscheinungsdatum:	23.10.2022
Gewicht:	0,341 kg