Value Functions on Simple Algebras, and Associated Graded Rings

“The book gives a good idea of the present state of valuation theory on division algebras and its applications, and also, of a new approach to this field worked out with the active participation of the authors … . It can be very useful to graduate students and research mathematicians interested in central simple algebras, Brauer groups, valuation theory and other related areas. Each chapter contains examples and exercises … .” (Ivan D. Chipchakov, zbMATH 1357.16002, 2017)

“This monograph offers a detailed exposition of graded central simple algebras over graded fields and central simple algebras over valued fields, emphasizing strong connections between the two theories. … The two authors, who took major part in the development of this new theory, are masters of precise exposition. Their book will surely serve as acornerstone of the theory of central simple algebras in the decades to come.” (Uzi Vishne, Mathematical Reviews, October, 2016)