Value functions on simple algebras, and associated graded rings
Jean-Pierre Tignol (Author), Adrian R. Wadsworth (Author)
This monograph is the first book-length treatment of valuation theory in finite-dimensional division algebras, a topic of active and substantial research over the past forty years. Its development was driven in the last decades of the 20th century by important advances such as Amitsur's construction of uncrossed products and Platonov's solution to the Tannaka-Artin problem. This study is particularly timely because it addresses the topic from the perspective of the associated graded structures. This new approach has been developed by the authors in recent years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as uncrossed products and indecomposable algebras. Furthermore, the use of valuation theory is shown in reduced calculations of the Whitehead group (after Hazrat and Wadsworth) and in calculations of essential dimensions (after Baek and Merkurjev). The target audience consists of graduate students and research mathematicians
eBook, English, 2015
Springer, Cham, 2015