Value Functions on Simple Algebras, and Associated Graded Rings

• Main Authors: Tignol, Jean-Pierre (Author), Wadsworth, Adrian R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Associative rings.; Rings (Algebra).; Algebra.; Field theory (Physics).; Associative Rings and Algebras.; Field Theory and Polynomials.

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's...

Table of Contents:

• Valuations on Division Rings
• Graded Algebra
• Value Functions
• Existence and Fundamental Properties of Gauges
• Graded and Valued Field Extensions
• Brauer Groups
• Total Ramifcation
• Division Algebras over Henselian Fields
• Subfields and Splitting Fields of Division Algebras
• Indecomposable Division Algebras
• Computation of SK1(D)
• The Essential Dimension of Central Simple Algebras.