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Hereditary orders in the quotient ring of a skew polynomial ring
(Maltepe Üniversitesi, 2009) Kauta, John S.
Let K be a field, and let ? be an automorphism of K of finite order, say n. One can form a skew polynomial ring K[X, ?] over K with the usual rules of multiplication defined by the commutation rule: Xa = ?(a)X ? a ? K. Let K(X, ?) denote the skew field of quotients of K[X, ?]. If F is the fixed field of ?, then K(X, ?) is a cyclic algebra of degree n with center F (Xn). If V is a valuation ring of F (Xn) containing F , and S is the integral closure of V in K(Xn), then any order of K(X, ?) with center V can be written as a “crossed-product V -algebra”