About: Principal root of unity

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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 -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. 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.

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  • 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 -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. 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. (en)
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  • 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 -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. 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. (en)
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  • Principal root of unity (en)
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