Real Algebra
A First Course
Please note that the standard 14-day cancellation right terminates upon receiving access to the e-book.
Product description
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 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.
Accessibility information
Select variation, to see accessibility information
Details
- ISBN13 9783031098000
- Released 2022
- Publisher Springer
- Format Elektronisk medie
- Language English