On Ramification Theory in Projective Orders

Abstract

The ramification theory in commutative rings, as a generalization of the classical one in maximal orders over a Dedekind domain, was established in [1], [13], [15] and etc.. For non-commutative algebras this was also studied in [3], [4], [9], [18] and etc.. However, the different theorem, which is a central part of ramification theory, has not been given in those, except for some special cases (cf. [12], [18]). The main object of this paper is to give the discriminant theorem and the different theorem for projective orders in a (non-commutative) separable algebra, in the most general form.