Title: Non-Commutative Valuation Rings and Semi-Hereditary Orders
Description: 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.
Subjects: Mathematics, Field theory (Physics), Algebra, Rings (algebra), Algebraic number theory, Associative Rings and Algebras, Order, Lattices, Ordered Algebraic Structures, Homological Algebra Category Theory, Commutative Rings and Algebras, Field Theory and Polynomials