Cyclic polynomials and the multiplication matrices of their roots

Let be an integrally closed, characteristic zero domain, its field of fractions, m 2 an integer and a cyclic polynomial. Let τ be a generator of and suppose the θi are labeled so that τ(θi)=θi+1 (indices mod m). Suppose that the discriminant is nonzero. For 0 i,j m−1, define the elements by θ0θi=∑j=0m−1ai,jθj. Let A=[ai,j]0 i,j