Principal root of unity

In mathematics, a principal n-th root of unity (where n is a positive integer) of a ring is an element

satisfying the equations In an integral domain, every primitive n-th root of unity is also a principal

in the ring of integers modulo

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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