Non-Commutative Valuation Rings and Semi-Hereditary Orders (K-Monographs in Mathematics)

This is the first self-contained summary of non-Noetherian orders in a simple Artinian ring, a subject in which much progress has been made in the last decade.
The contents of the book are mainly Dubrovin valuation rings and semi-hereditary orders, including Prüfer and semi-local Bezout orders, which are considered, in a sense, as global theories of Dubrovin valuation rings. These are then developed further, and applied to give some examples such as Dubrovin valuation rings in crossed product algebras, semi-hereditary maximal order in certain matrix rings, and the idealizers of semi-hereditary orders and Henselization of Bezout orders.
Audience: This volume will be of interest to researchers and graduate students whose work involves non-commutative ring theory and module theory.