EXTREMAL ORDERS INSIDE SIMPLE ARTINIAN RINGS

Document Type: Regular Paper

Author

84 Manburgh Tce, Darra, QLD 4076, Australia

Abstract

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

Keywords