 The last example does not generalize directly to other moduli. However for any modulus that is a power \(p^n\) of a prime, it can be shown that there exists a unique multiplication making the group \(Z_{p^n}\) a ring in a way that makes the nonzero elements of the ring a cyclic (and therefore abelian) group under the multiplication, and hence making the ring a field. The fields constructed in this way are the only finite fields.