Question

Find two non isomorphic galois extensions of degree three of $Q(z_6)$

score 80 · Answer 1 · 2019-11-28 17:22:02

80

Views

Find two non isomorphic galois extensions of degree three of $Q(z_6)$

Published on 28 Nov 2019 - 17:22

score 142 · Answer 2 · 2026-03-30 17:05:14

142

Views

If $L/K$ is a non-trivial radical extension then there exists a prime $p$ and an $\alpha \in L$ such that $\alpha \notin K$ but $\alpha^p \in K$

Published on 30 Mar 2026 - 17:05

score 139 · Answer 3 · 2026-04-01 06:30:26

139

Views

Which "elements", when added, will create a field extension to a finite field?

Published on 01 Apr 2026 - 6:30

score 167 · Answer 4 · 2026-03-29 13:40:55

167

Views

Irreducible cubic polynomial in $\mathbb{Q}[x]$ has no roots in $\mathbb{Q}(\sqrt{2}, 5^{1/4})$

Published on 29 Mar 2026 - 13:40

score 50 · Answer 5 · 2019-11-30 10:41:58

50

Views

Find a minimal polynomial of element

Published on 30 Nov 2019 - 10:41

score 443 · Answer 6 · 2026-03-25 15:42:25

443

Views

Galois group $G_{L/K}$ of unramified extension and its residue fields

Published on 25 Mar 2026 - 15:42

score 25 · Answer 7 · 2026-04-01 06:30:20

25

Views

Can we adjoin the fourth roots of $x$?

Published on 01 Apr 2026 - 6:30

score 128 · Answer 8 · 2019-12-01 21:50:37

128

Views

The field of fractions of an order is $\mathbb{Q}$

Published on 01 Dec 2019 - 21:50

score 212 · Answer 9 · 2026-03-25 04:40:59

212

Views

Find the ring of integers of $\mathbb{Q}(\theta)$

Published on 25 Mar 2026 - 4:40

score 184 · Answer 10 · 2026-03-30 17:03:23

184

Views

If $M/K$ and $L/K$ are both radical extensions then $L/M$ is a radical extension

Published on 30 Mar 2026 - 17:03

score 56 · Answer 11 · 2026-04-01 06:35:01

56

Views

The existence of the normal subgroups of GF($2^m$) under addition

Published on 01 Apr 2026 - 6:35

score 227 · Answer 12 · 2019-12-03 07:43:58

227

Views

the product of a constructible number and a non-constructible number is constructible or not?

Published on 03 Dec 2019 - 7:43

score 657 · Answer 13 · 2026-03-31 19:16:46

657

Views

How to show that $\mathbb{Q}(\alpha) = \left\{ p+q\alpha+r\alpha^2 \mid p, q, r\in \mathbb{Q} \right\}$, where $\alpha$ is the real cube root of $2$?

Published on 31 Mar 2026 - 19:16

score 355 · Answer 14 · 2019-12-04 20:04:11

355

Views

$K$ is algebraically closed in $K(x_1, \ldots, x_n)$.

Published on 04 Dec 2019 - 20:04

score 18 · Answer 15 · 2026-02-23 04:57:25

18

Views

$[F(a):F(a^i)](y_1+...+y_m)=x_1^i+...+x_n^i$

Published on 23 Feb 2026 - 4:57

List Question

Find two non isomorphic galois extensions of degree three of $Q(z_6)$

If $L/K$ is a non-trivial radical extension then there exists a prime $p$ and an $\alpha \in L$ such that $\alpha \notin K$ but $\alpha^p \in K$

Which "elements", when added, will create a field extension to a finite field?

Irreducible cubic polynomial in $\mathbb{Q}[x]$ has no roots in $\mathbb{Q}(\sqrt{2}, 5^{1/4})$

Find a minimal polynomial of element

Galois group $G_{L/K}$ of unramified extension and its residue fields

Can we adjoin the fourth roots of $x$?

The field of fractions of an order is $\mathbb{Q}$

Find the ring of integers of $\mathbb{Q}(\theta)$

If $M/K$ and $L/K$ are both radical extensions then $L/M$ is a radical extension

The existence of the normal subgroups of GF($2^m$) under addition

the product of a constructible number and a non-constructible number is constructible or not?

How to show that $\mathbb{Q}(\alpha) = \left\{ p+q\alpha+r\alpha^2 \mid p, q, r\in \mathbb{Q} \right\}$, where $\alpha$ is the real cube root of $2$?

$K$ is algebraically closed in $K(x_1, \ldots, x_n)$.

$[F(a):F(a^i)](y_1+...+y_m)=x_1^i+...+x_n^i$

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