root of unity

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root of unity

[¦rüt əv ′yü·nəd·ē]

(mathematics)

A root of unity in a field F is an element a in F such that a ⁿ= 1 for some positive integer n.

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Throughout this work we assume that if p [member of] I then p is not a root of unity, so that we always have [I.

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The equation F([omega]) = 0 is an algebraic equation with rational coefficients in the unknown (omega); hence, if some primitive d-th root of unity satisfies it, then every primitive d-th root of unity satisfies it.

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Fix once and for all a primitive nth root of unity [zeta].

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When q is a root of unity, its image under the specialization [bar.

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Let [xi] be a primitive m-th root of unity, and [[mu].

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th] root of unity in a field F of characteristic zero (so necessarily l [greater than or equal to] 2).

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We assume that K contains a primitive [absolute value of G]-th root of unity and that k is algebraically closed.