A commutative ring without zero divisors in which the ideal classes form a group is called a Dedekind ring. In such a ring every irreducible ideal is maximal and therefore a prime ideal and every ideal can be decomposed uniquely into prime ideals. In all that follows 0 will denote the quotient field of a Dedekind ring 3, 0' a separable algebraic extension of degree n of a and $' the ring of all elements of !' which satisfy monic equations with coefficients in S. The elements of a and a' will be called the integers of W and a' respectively. A set of n elements co, c o ., w) of a' such that every element of 3' can be written in the form