Question

Understanding problem in proof that $\{1,\zeta,...,\zeta^{p-2}\}$ is an integral basis for ring of algebraic integers in $\mathbb{Q}(\zeta)$

score 244 · Answer 1 · 2017-12-16 23:25:27

Understanding problem in proof that $\{1,\zeta,...,\zeta^{p-2}\}$ is an integral basis for ring of algebraic integers in $\mathbb{Q}(\zeta)$

score 362 · Answer 2 · 2017-12-19 00:27:14

362

Views

Examples of cyclotomic extensions with Galois group not isomorphic to $U(\mathbb{Z}_n)$

Published on 19 Dec 2017 - 0:27

score 125 · Answer 3 · 2017-12-23 02:21:06

125

Views

Relation between class numbers of $\mathbb{Q}(\sqrt{pm})$ and $\mathbb{Q}(\sqrt{-m})$

Published on 23 Dec 2017 - 2:21

score 251 · Answer 4 · 2017-12-24 17:25:38

251

Views

Non-Monic polynomials with the same discriminant as the cyclotomic polynomial.

Published on 24 Dec 2017 - 17:25

score 166 · Answer 5 · 2026-03-25 00:48:13

166

Views

Cyclotomic integers

Published on 25 Mar 2026 - 0:48

score 544 · Answer 6 · 2011-12-22 15:44:02

544

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For which $n\in\mathbf{N}$ do we have $\mathbf{Q}(z_{5},z_{7}) = \mathbf{Q}(z_{n})$?

Published on 22 Dec 2011 - 15:44

score 2k · Answer 7 · 2011-12-23 15:02:46

2k

Views

Elementary proof of $\mathbb{Q}(\zeta_n)\cap \mathbb{Q}(\zeta_m)=\mathbb{Q}$ when $\gcd(n,m)=1$.

Published on 23 Dec 2011 - 15:02

score 3.8k · Answer 8 · 2013-02-10 14:52:03

3.8k

Views

Is $\sqrt 7$ a sum of roots of unity?

Published on 10 Feb 2013 - 14:52

score 60 · Answer 9 · 2020-08-03 10:09:13

60

Views

find algebraic integers in $\mathbb{Q}[x]$ where x is a root of unity

Published on 03 Aug 2020 - 10:09

score 75 · Answer 10 · 2020-08-09 14:57:18

75

Views

Find the Subfield diagram of splitting field of $x^{33}-1$ over $\mathbb{Q}$

Published on 09 Aug 2020 - 14:57

score 85 · Answer 11 · 2020-08-14 13:33:46

85

Views

Euler Systems and Coleman’s Conjecture

Published on 14 Aug 2020 - 13:33

score 31 · Answer 12 · 2020-08-18 21:18:34

31

Views

Find the minimal polynomial of the 18th root of unity and the Galois group of $\mathbb{Q}(z_{18})$ and its generators

Published on 18 Aug 2020 - 21:18

score 164 · Answer 13 · 2020-09-14 09:00:19

164

Views

Artin conductor of cyclotomic extensions.

Published on 14 Sep 2020 - 9:00

score 88 · Answer 14 · 2020-10-08 17:47:34

88

Views

Understanding action of $(\mathbb Z_p/(p^n))^ \times$ in Lubin Tate formal group laws context on $\mathbb{Q}_p[\zeta_{p^r}]$

Published on 08 Oct 2020 - 17:47

score 245 · Answer 15 · 2020-10-08 20:46:22

245

Views

Galois group of $\mathbb{Q}(\zeta_p)/\mathbb{Q}(\sqrt{p})$

Published on 08 Oct 2020 - 20:46

List Question

Understanding problem in proof that $\{1,\zeta,...,\zeta^{p-2}\}$ is an integral basis for ring of algebraic integers in $\mathbb{Q}(\zeta)$

Examples of cyclotomic extensions with Galois group not isomorphic to $U(\mathbb{Z}_n)$

Relation between class numbers of $\mathbb{Q}(\sqrt{pm})$ and $\mathbb{Q}(\sqrt{-m})$

Non-Monic polynomials with the same discriminant as the cyclotomic polynomial.

Cyclotomic integers

For which $n\in\mathbf{N}$ do we have $\mathbf{Q}(z_{5},z_{7}) = \mathbf{Q}(z_{n})$?

Elementary proof of $\mathbb{Q}(\zeta_n)\cap \mathbb{Q}(\zeta_m)=\mathbb{Q}$ when $\gcd(n,m)=1$.

Is $\sqrt 7$ a sum of roots of unity?

find algebraic integers in $\mathbb{Q}[x]$ where x is a root of unity

Find the Subfield diagram of splitting field of $x^{33}-1$ over $\mathbb{Q}$

Euler Systems and Coleman’s Conjecture

Find the minimal polynomial of the 18th root of unity and the Galois group of $\mathbb{Q}(z_{18})$ and its generators

Artin conductor of cyclotomic extensions.

Understanding action of $(\mathbb Z_p/(p^n))^ \times$ in Lubin Tate formal group laws context on $\mathbb{Q}_p[\zeta_{p^r}]$

Galois group of $\mathbb{Q}(\zeta_p)/\mathbb{Q}(\sqrt{p})$

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