Principal root of unity
In mathematics, a principal n-th root of unity of a ring is an element satisfying the equations
In an integral domain, every primitive n-th root of unity is also a principal -th root of unity. In any ring, if is a power of, then any -th root of is a principal -th root of unity.
A non-example is in the ring of integers modulo ; while and thus is a cube root of unity, meaning that it is not a principal cube root of unity.
The significance of a root of unity being principal is that it is a necessary condition for the theory of the discrete Fourier transform to work out correctly.
