In mathematics, a principal n-th root of unity (where n is a positive integer) of a ring satisfying the equations

In an integral domain, every primitive n-th root of unity-th root of unity. In any ring, if n is a power of 2, then any n/2-th root of −1 is a principal n-th root of unity.

in the 26 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.

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