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What exactly is an $n$-th root in a field?

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#abstract-algebra #field-theory #finite-fields #roots-of-unity
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Primitive $p$-th root of unity with characteristic $p$

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#field-theory #finite-fields #extension-field #roots-of-unity #primitive-roots
197
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The system $2XY+X^2+Y^2+X^2Y+Y+XY^2+X=0$, for distinct pairs $X, Y\in\{J, K, L\}$ for $n$th roots of unity $J, K, L$.

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#nonlinear-system #roots-of-unity
1.4k
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Root of unity belongs to Z/qZ. How?

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#roots-of-unity #primitive-roots #cyclotomic-polynomials #cyclotomic-fields
484
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Complex Partial Fraction Decomposition

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#polynomials #complex-numbers #partial-fractions #roots-of-unity
62
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An interesting property of the roots

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#roots #roots-of-unity
226
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Primitive roots of unity and $I$-adically separated rings.

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#abstract-algebra #ring-theory #commutative-algebra #ideals #roots-of-unity
149
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Closed formula for $\Phi'_n(\zeta)$ as complex number

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#complex-numbers #roots-of-unity #cyclotomic-polynomials
114
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Finding roots of unity

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#complex-analysis #roots-of-unity
47
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An Upper and Lower Bound for a Field Extension of $\mathbb{Q}$ by a Complex Root

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#extension-field #roots-of-unity #separable-extension
77
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Summation involving Roots of Unity

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#complex-numbers #summation #roots-of-unity
62
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Solving roots of unity

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#roots-of-unity
904
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For what integers $n$ is $-1$ an $n$th root of unity?

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#abstract-algebra #complex-numbers #roots-of-unity
267
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If $\zeta_n$ is the $nth$ root of unity, find $\dim_{\Bbb Q}\Bbb Q[\zeta_n]$

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#vector-spaces #roots-of-unity
197
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If $\zeta_n$ is a primitive $n$th root of unity, why is $\text{dim}_{\Bbb Q}\Bbb Q[\zeta_n]=\phi(n)$?

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#vector-spaces #roots-of-unity

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