Prime Divisors and Noncommutative Valuation Theory

Describes different generalizations of valuations from the common generalized concept of primes in algebras Combines the arithmetic of finite dimensional central simple algebras with new theory for infinite dimensional ones Mixing methods concerning value functions, valuation filtrations and orders over valuation rings for the study of new classes of algebras, e.g. quantized algebras, Weyl algebras and Hopf algebras Includes supplementary material: sn.pub/extras