List questions from cyclotomic-fields

Published on 08 Sep 2022 - 9:23

61

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How to prove that: Automorphism $\zeta_n\to\zeta_n^p$ leaves prime ideal factor of p unchanged.

Published on 16 Sep 2022 - 15:14

108

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explicit generators for the unit group of a cyclotomic field

Published on 04 Nov 2022 - 21:34

62

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Is the norm of a principal prime ideal principal?

Published on 12 Nov 2022 - 15:35

117

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Which $ \sqrt{n} $ are in a particular cyclotomic field

Published on 18 Nov 2022 - 13:22

52

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Primes above $2$ in cyclotomic fields

Published on 18 Nov 2022 - 17:59

91

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Coprime ideals and Dedekind zeta function over cyclotomic fields

Published on 20 Nov 2022 - 17:31

121

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Parity of the class number of cyclotomic fields

Published on 25 Mar 2026 - 10:57

52

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$[L:K]$ is a Galois extention with Galois group G. Describe a map G to $\Bbb Z/p\Bbb Z$

Published on 04 Dec 2022 - 8:40

32

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$\xi_p^i-\xi_p^j$ divides $p$ in the ring $\mathbb{Z}[\xi_p]$

Published on 09 Dec 2022 - 18:41

646

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Can every algebraic number be written in terms of roots of unity?

Published on 12 Dec 2022 - 4:26

84

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How to prove $x^p+y^p=\displaystyle{\prod_{k=0}^{p-1} (x+\xi_p^ky)}$

Published on 14 Dec 2022 - 8:42

39

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$\sigma(\overline{z})=\overline{\sigma(z)}$ with $\sigma$ $\mathbb{Q}$-automorphism

Published on 29 Dec 2022 - 10:38

46

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Prove $1-\xi_p$ is irreducible in $\mathbb{Z}[\xi_p]$

Published on 29 Dec 2022 - 18:48

189

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$\mathbb{Q}(\sqrt{-23}) \subseteq \mathbb{Q}(\zeta_{23})$

Published on 03 Jan 2023 - 7:03

List Question

If $P(P(x))=x^{36}$, does it imply $P(x)=x^6$?

How to prove that: Automorphism $\zeta_n\to\zeta_n^p$ leaves prime ideal factor of p unchanged.

explicit generators for the unit group of a cyclotomic field

Is the norm of a principal prime ideal principal?

Which $ \sqrt{n} $ are in a particular cyclotomic field

Primes above $2$ in cyclotomic fields

Coprime ideals and Dedekind zeta function over cyclotomic fields

Parity of the class number of cyclotomic fields

$[L:K]$ is a Galois extention with Galois group G. Describe a map G to $\Bbb Z/p\Bbb Z$

$\xi_p^i-\xi_p^j$ divides $p$ in the ring $\mathbb{Z}[\xi_p]$

Can every algebraic number be written in terms of roots of unity?

How to prove $x^p+y^p=\displaystyle{\prod_{k=0}^{p-1} (x+\xi_p^ky)}$

$\sigma(\overline{z})=\overline{\sigma(z)}$ with $\sigma$ $\mathbb{Q}$-automorphism

Prove $1-\xi_p$ is irreducible in $\mathbb{Z}[\xi_p]$

$\mathbb{Q}(\sqrt{-23}) \subseteq \mathbb{Q}(\zeta_{23})$

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