Real algebra : a first course / Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger ; translated by Thomas Unger.

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Real algebra : a first course / Manfred Knebusch, Claus Scheiderer ; with contributions by Thomas Unger ; translated by Thomas Unger.

Einführung in die reelle Algebra. English

9783031098000 (electronic bk.)
3031098005 (electronic bk.)
9783031097997
3031097998

Cham : Springer, [2022]

©2022

English

Translated from German.

1 online resource (xii, 206 pages) : illustrations.

10.1007/978-3-031-09800-0 doi

QA152.3

512.9

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 Einfuhrung 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 geometryas far as they are directly related to the contents of the earlier chapterssince 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.

Includes bibliographical references and indexes.

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Description based on print version record.

Universitext.

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