Hereditary orders in the quotient ring of a skew polynomial ring

Abstract

Let K be a field, and let σ be an automorphism of K of finite order. Let K(X; σ) be the quotient ring of the skew polynomial ring K[X; σ]. Then any order in K(X; σ) which contains K and its center is a valuation ring of the center of K(X; σ) is a crossed-product algebra Af, where f is some normalized 2-cocycle. Associated to f is a subgroup H of [σ] and a graph. In this paper, we determine the connections between hereditary-ness and maximal order properties of Af and the properties of H, f and the graph of f.