Real Algebra

​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.

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

"More than 30 years after its initial publication, the present textbook is still a very valuable source for results in real algebra. It can serve as a textbook for a university course, but also experts will benefit from the nice account of concepts and results. It's great that the book is available again, in particular in an English translation for an international audience." (Tim Netzer, zbMATH 1505.13001, 2023)

“More than 30 years after its initial publication, the present textbook is still a very valuable source for results in real algebra. It can serve as a textbook for a university course, but also experts will benefit from the nice account of concepts and results. It’s great that the book is available again, in particular in an English translation for an international audience.” (Tim Netzer, zbMATH 1505.13001, 2023)