On number theoretic Fourier transforms in residue class rings

The proof of the orthogonality conditions that must be fulfilled by the transform factor α of a NTFT of length N, is based upon the possibility of cancelling all nonzero factors of the form (α^q- 1), q = 1, 2,..., N - 1. In a residue ring containing zero divisors, this is not allowed, unless all such factors can be shown not to be divisors of zero. It is shown that this is the case, when a is any primitive Nth root of unity, N being an allowed transform legnth. At the same time, a property is established that helps to reduce the amount of searching needed to find suitable transform factors.