Question

Basis of field - polynomial

score 418 · Answer 1 · 2014-05-29 22:41:09

418

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Basis of field - polynomial

Published on 29 May 2014 - 22:41

score 1k · Answer 2 · 2026-03-25 14:25:55

1k

Views

A Galois Extension over a field of characteristic p

Published on 25 Mar 2026 - 14:25

score 1.1k · Answer 3 · 2014-06-01 02:50:20

1.1k

Views

Multiplicative Property of the degree of field extension

Published on 01 Jun 2014 - 2:50

score 3.2k · Answer 4 · 2026-03-26 06:25:37

3.2k

Views

Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

Published on 26 Mar 2026 - 6:25

score 283 · Answer 5 · 2014-06-01 18:55:27

283

Views

$\mathbb{Q}(\zeta_7)$ subextension of degree $3$

Published on 01 Jun 2014 - 18:55

score 572 · Answer 6 · 2014-06-02 07:22:03

572

Views

Extending Automorphisms, Isomorphisms

Published on 02 Jun 2014 - 7:22

score 145 · Answer 7 · 2014-06-02 10:07:58

145

Views

How to prove that $\mathbb{Q}(\sqrt[3]{2}+\sqrt{3})=\mathbb{Q}(\sqrt[3]{2},\sqrt{3})$?

Published on 02 Jun 2014 - 10:07

score 39 · Answer 8 · 2014-06-02 15:04:32

39

Views

Find the minimal polynomial of $z=u+i \in \mathbb{C}$ in $\mathbb{Q}$ where $u=\sqrt{7}$

Published on 02 Jun 2014 - 15:04

score 107 · Answer 9 · 2014-06-02 17:03:34

107

Views

Find all the subfields $\mathbb{K}$ in $\mathbb{C}$ such that $\mathbb{K}$ and $\mathbb{Q}(i)$ are isomorphic

Published on 02 Jun 2014 - 17:03

score 318 · Answer 10 · 2014-06-03 17:43:20

318

Views

Find the Galois group

Published on 03 Jun 2014 - 17:43

score 439 · Answer 11 · 2014-06-03 18:17:18

439

Views

Prove that if $p$ is prime then $\frac{X^p-1}{X-1}=X^{p-1}+\cdots+X+1$ is irreducbile in $\mathbb{Q}[X]$.

Published on 03 Jun 2014 - 18:17

score 36 · Answer 12 · 2014-06-03 19:09:15

36

Views

Prove that for all $n \ge 2$ there exist finite field extensions of $\mathbb{Q}$ of dimension $n$.

Published on 03 Jun 2014 - 19:09

score 55 · Answer 13 · 2014-06-03 19:38:55

55

Views

Given $u=e^{i2\pi\over{7}}$, determine whether $\mathbb{Q}(u)/\mathbb{Q}$ is a Galois extension

Published on 03 Jun 2014 - 19:38

score 59 · Answer 14 · 2014-06-05 03:46:31

59

Views

What's $[L:K(\alpha)]$ here?

Published on 05 Jun 2014 - 3:46

score 1.3k · Answer 15 · 2026-03-26 02:54:02

1.3k

Views

For $a=\cos(2\pi/n)$, show that $[\mathbb{Q}(a):\mathbb{Q}] = \ldots$

Published on 26 Mar 2026 - 2:54

List Question

Basis of field - polynomial

A Galois Extension over a field of characteristic p

Multiplicative Property of the degree of field extension

Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

$\mathbb{Q}(\zeta_7)$ subextension of degree $3$

Extending Automorphisms, Isomorphisms

How to prove that $\mathbb{Q}(\sqrt[3]{2}+\sqrt{3})=\mathbb{Q}(\sqrt[3]{2},\sqrt{3})$?

Find the minimal polynomial of $z=u+i \in \mathbb{C}$ in $\mathbb{Q}$ where $u=\sqrt{7}$

Find all the subfields $\mathbb{K}$ in $\mathbb{C}$ such that $\mathbb{K}$ and $\mathbb{Q}(i)$ are isomorphic

Find the Galois group

Prove that if $p$ is prime then $\frac{X^p-1}{X-1}=X^{p-1}+\cdots+X+1$ is irreducbile in $\mathbb{Q}[X]$.

Prove that for all $n \ge 2$ there exist finite field extensions of $\mathbb{Q}$ of dimension $n$.

Given $u=e^{i2\pi\over{7}}$, determine whether $\mathbb{Q}(u)/\mathbb{Q}$ is a Galois extension

What's $[L:K(\alpha)]$ here?

For $a=\cos(2\pi/n)$, show that $[\mathbb{Q}(a):\mathbb{Q}] = \ldots$

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