CROSSED PRODUCT ORDERS AND NONCOMMUTATIVE ARITHMETIC

[摘要] Let LAMBDA = (S/R, h) be a crossed product order (CPO) in the crossed product algebra A = (L/K, h) with integer factor set h. Studying the chain of orders LAMBDA0 := LAMBDA, LAMBDA(i+1): = O(l) (rad LAMBDA(i)) we give, in the local case, a measure of the deviation from the CPO to its hereditary hull and can thus classify all hereditary local CPOs. In the local case there exists a unique optimal CPO and we show how to optimize a given factor set. If the extension L/K is also tamely ramified we can compute the Schur index of A by the values of the factor set. Studying the semilocal and the global case we give necessary criteria for hereditary CPOs and solve the heredity question completely for cyclic CPOs. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-01