Question

Find the minimal polynomial of $\alpha=(1-\omega)/2$ over $\mathbb{Q}$ where $\omega$ is a primitive 8th root of unity

score 181 · Answer 1 · 2016-04-17 15:17:41

181

Views

Find the minimal polynomial of $\alpha=(1-\omega)/2$ over $\mathbb{Q}$ where $\omega$ is a primitive 8th root of unity

Published on 17 Apr 2016 - 15:17

score 719 · Answer 2 · 2016-04-22 03:06:46

719

Views

Which cyclotomic fields are different?

Published on 22 Apr 2016 - 3:06

score 1.4k · Answer 3 · 2016-04-23 06:23:23

1.4k

Views

On the degree of cyclotomic fields extension.

Published on 23 Apr 2016 - 6:23

score 222 · Answer 4 · 2016-05-12 09:02:56

222

Views

Question about S.Lang's proof of Kummer's Lemma

Published on 12 May 2016 - 9:02

score 498 · Answer 5 · 2016-05-29 18:14:19

498

Views

Regarding the unique subfields of a cyclotomic field extension

Published on 29 May 2016 - 18:14

score 1.3k · Answer 6 · 2016-05-31 17:55:23

1.3k

Views

Prove that the $7$-th cyclotomic extension $\mathbb{Q}(\zeta_7)$ contains $\sqrt{-7}$

Published on 31 May 2016 - 17:55

score 218 · Answer 7 · 2016-06-02 00:07:07

218

Views

Describe the structure $\operatorname{Gal}(\mathbb{Q}(\zeta_4)/\mathbb{Q})$

Published on 02 Jun 2016 - 0:07

score 1.2k · Answer 8 · 2016-06-08 13:55:53

1.2k

Views

Solutions to a quadratic diophantine equation $x^2 + xy + y^2 = 3r^2$.

Published on 08 Jun 2016 - 13:55

score 264 · Answer 9 · 2016-06-10 18:33:24

264

Views

Understanding a proof in Washington's "Cyclotomic Fields"

Published on 10 Jun 2016 - 18:33

score 1.1k · Answer 10 · 2013-08-21 09:25:24

1.1k

Views

Let $f(x)=x^8-16$. Determine the Galois group of the splitting field of $f(x)$ over the fields $\Bbb{Q}$ and $\Bbb{Z}_{17}$.

Published on 21 Aug 2013 - 9:25

score 1.7k · Answer 11 · 2013-10-17 17:58:10

1.7k

Views

Ramified prime in cyclotomic extension of a number field

Published on 17 Oct 2013 - 17:58

score 365 · Answer 12 · 2017-04-14 08:05:44

365

Views

Class number of the compositum of a quadratic extension of a cyclotomic field

Published on 14 Apr 2017 - 8:05

score 357 · Answer 13 · 2017-04-14 12:42:57

357

Views

Describe the real elements of a Cyclotomic Extension under an Embedding

Published on 14 Apr 2017 - 12:42

score 840 · Answer 14 · 2017-04-21 16:28:12

840

Views

Let $d\in \mathbb Q$ , to prove $\mathbb Q(\sqrt d) \subseteq \mathbb Q(e^{2i\pi/n})$ for some positive integer $n$ (without Kronecker-Weber)

Published on 21 Apr 2017 - 16:28

score 48 · Answer 15 · 2017-04-25 16:19:00

48

Views

$a_n:=e^{2\pi i/n} $ , then how to show that $[\mathbb Q(a_n):\mathbb Q(a_n +1/a_n)]=2$ ?

Published on 25 Apr 2017 - 16:19

List Question

Find the minimal polynomial of $\alpha=(1-\omega)/2$ over $\mathbb{Q}$ where $\omega$ is a primitive 8th root of unity

Which cyclotomic fields are different?

On the degree of cyclotomic fields extension.

Question about S.Lang's proof of Kummer's Lemma

Regarding the unique subfields of a cyclotomic field extension

Prove that the $7$-th cyclotomic extension $\mathbb{Q}(\zeta_7)$ contains $\sqrt{-7}$

Describe the structure $\operatorname{Gal}(\mathbb{Q}(\zeta_4)/\mathbb{Q})$

Solutions to a quadratic diophantine equation $x^2 + xy + y^2 = 3r^2$.

Understanding a proof in Washington's "Cyclotomic Fields"

Let $f(x)=x^8-16$. Determine the Galois group of the splitting field of $f(x)$ over the fields $\Bbb{Q}$ and $\Bbb{Z}_{17}$.

Ramified prime in cyclotomic extension of a number field

Class number of the compositum of a quadratic extension of a cyclotomic field

Describe the real elements of a Cyclotomic Extension under an Embedding

Let $d\in \mathbb Q$ , to prove $\mathbb Q(\sqrt d) \subseteq \mathbb Q(e^{2i\pi/n})$ for some positive integer $n$ (without Kronecker-Weber)

$a_n:=e^{2\pi i/n} $ , then how to show that $[\mathbb Q(a_n):\mathbb Q(a_n +1/a_n)]=2$ ?

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