EXTREMAL ORDERS INSIDE SIMPLE ARTINIAN RINGS

Abstract

The aim of this paper is to study orders over a valuation ring V with arbitrary rank in acentral simple F-algebra Q. The relation between all of the orders is explained with a diagram. It is thenshown that inside Bezout order, extremal V-orders are precisely semi-hereditary. In the last section, theeffect of Henselization on maximal and semi-hereditary orders is examined.