List questions from cyclotomic-fields

Published on 25 Mar 2026 - 12:26

454

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"Frobenius element" in cyclotomic extension for ramified primes

Published on 27 Dec 2016 - 19:08

479

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If a cyclotomic integer has (rational) prime norm, is it a prime element?

Published on 28 Dec 2016 - 7:49

290

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Automorphisms of infinite cyclotomic extension field

Published on 28 Dec 2016 - 12:12

61

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Prove that no integer $w$ exists such that the splitting field of $x^4+x^3+x^2+x+1+w$ is that of $x^4+x^3+x^2+x+1$.

Published on 23 Feb 2017 - 5:44

307

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Discriminant of an almost cyclotomic field

Published on 03 Mar 2017 - 17:59

108

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Cyclotomic Extension

Published on 21 Mar 2017 - 18:16

52

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Field extension $\Bbb Q (\zeta_p)$

Published on 22 Mar 2017 - 1:44

753

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Show that algebraic integers in $\mathbb{Q}[\zeta_3]$ are exactly $\mathbb{Z}[\zeta_3]$.

Published on 25 Mar 2026 - 6:24

87

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How to show the degree $[\Bbb Q(\alpha _n+\frac{1}{\alpha_n}) : \Bbb Q]$ is $\phi(n)/2$, where $\alpha_n$ is a primitive $n$-th root of unity?

Published on 29 Mar 2017 - 15:19

126

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$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

Published on 11 Mar 2023 - 15:16

67

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Generator of ideal in $Q(\zeta_5)$

Published on 31 Mar 2023 - 0:38

33

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Sign of image of square root under automorphism of cyclotomic extension

Published on 09 Apr 2023 - 19:19

80

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Implementation of the cyclotomic numbers

Published on 11 Apr 2023 - 13:27

30

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What is known about the minimal absolute value in $\mathbb{Z}[\zeta_n]\setminus\{0\}$?

Published on 23 Feb 2026 - 13:03

List Question

Determinant of prime cyclotomic field.

"Frobenius element" in cyclotomic extension for ramified primes

If a cyclotomic integer has (rational) prime norm, is it a prime element?

Automorphisms of infinite cyclotomic extension field

Prove that no integer $w$ exists such that the splitting field of $x^4+x^3+x^2+x+1+w$ is that of $x^4+x^3+x^2+x+1$.

Discriminant of an almost cyclotomic field

Cyclotomic Extension

Field extension $\Bbb Q (\zeta_p)$

Show that algebraic integers in $\mathbb{Q}[\zeta_3]$ are exactly $\mathbb{Z}[\zeta_3]$.

How to show the degree $[\Bbb Q(\alpha _n+\frac{1}{\alpha_n}) : \Bbb Q]$ is $\phi(n)/2$, where $\alpha_n$ is a primitive $n$-th root of unity?

$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

Generator of ideal in $Q(\zeta_5)$

Sign of image of square root under automorphism of cyclotomic extension

Implementation of the cyclotomic numbers

What is known about the minimal absolute value in $\mathbb{Z}[\zeta_n]\setminus\{0\}$?

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