Prime Divisors and Noncommutative Valuation Theory

• Main Authors: Marubayashi, Hidetoshi (Author), Van Oystaeyen, Fred (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Lecture Notes in Mathematics, 2059
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Associative rings.; Rings (Algebra).; Geometry.; Algebraic Geometry.; Associative Rings and Algebras.

Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves.  But the noncommutative equivalent is mainly applied to finite dimensional skewfields.  Recently however, new types of algebras have become popul...

Table of Contents:

• 1. General Theory of Primes
• 2. Maximal Orders and Primes
• 3. Extensions of Valuations to some Quantized Algebras.