19898

EXTREMAL ORDERS INSIDE SIMPLE ARTINIAN RINGS

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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

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