List questions from cyclotomic-fields

Published on 13 Sep 2015 - 17:29

304

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How to think about Galois groups in a geometric way?

Published on 30 Sep 2015 - 14:07

135

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Show that $\frac{1-\zeta_p^k}{1-\zeta_p^j}$ is invertible in $\mathbb{Z}[\zeta_p]$

Published on 09 Oct 2015 - 10:21

89

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Prime that splits but not completely in $\mathbb{Q}(\zeta_{20})/\mathbb{Q}$

Published on 16 Oct 2015 - 11:49

173

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Of sum of cosines and the $7$th roots of unity

Published on 21 Oct 2015 - 23:19

201

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How to find an automorphism to enumerate the subfields of this cyclotomic field?

Published on 06 Mar 2026 - 20:35

290

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Unit of $\mathbb Q(\zeta_7)$ of infinite order

Published on 10 Nov 2015 - 22:49

366

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A subfield of $\mathbb{Q}(\zeta_{pq})$ with some ramification conditions

Published on 30 Dec 2015 - 13:53

351

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For what integer values of n is $\tan (\pi /n)$ an algebraic integer?

Published on 08 Mar 2026 - 4:31

696

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Minimal cyclotomic field containing a given quadratic field?

Published on 18 Jan 2016 - 14:34

658

Views

Is 5 a prime element in the cyclotomic ring of integers?

Published on 21 Mar 2016 - 21:24

984

Views

Proof of Kummer's Lemma in S. Langs 'Cyclotomic fields'

Published on 29 Mar 2016 - 12:58

113

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What's the sense behind that lemma?

Published on 30 Mar 2016 - 10:21

1.8k

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Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$

Published on 24 Mar 2026 - 15:58

477

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Minimal polynomial of root of unity over quadratic field

Published on 05 Apr 2016 - 20:49

List Question

when is $\mathbb{Q}(\mu_{2N})$ equal to $\mathbb{Q}(\mu_N)$?

How to think about Galois groups in a geometric way?

Show that $\frac{1-\zeta_p^k}{1-\zeta_p^j}$ is invertible in $\mathbb{Z}[\zeta_p]$

Prime that splits but not completely in $\mathbb{Q}(\zeta_{20})/\mathbb{Q}$

Of sum of cosines and the $7$th roots of unity

How to find an automorphism to enumerate the subfields of this cyclotomic field?

Unit of $\mathbb Q(\zeta_7)$ of infinite order

A subfield of $\mathbb{Q}(\zeta_{pq})$ with some ramification conditions

For what integer values of n is $\tan (\pi /n)$ an algebraic integer?

Minimal cyclotomic field containing a given quadratic field?

Is 5 a prime element in the cyclotomic ring of integers?

Proof of Kummer's Lemma in S. Langs 'Cyclotomic fields'

What's the sense behind that lemma?

Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$

Minimal polynomial of root of unity over quadratic field

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