Question

Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$

score 991 · Answer 1 · 2015-07-17 22:43:12

991

Views

Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$

Published on 17 Jul 2015 - 22:43

score 612 · Answer 2 · 2015-07-19 00:34:05

612

Views

$K/F$ Galois Extension, $H \leq G$, where $G$ the Galois group, then there is $\alpha \in K$ s.t. $H=\{\sigma \in G : \sigma \alpha = \alpha\}$.

Published on 19 Jul 2015 - 0:34

score 72 · Answer 3 · 2015-07-19 06:53:37

72

Views

Why the extension dimension of $x^3-2$ equal to $6$?

Published on 19 Jul 2015 - 6:53

score 179 · Answer 4 · 2015-07-19 07:22:46

179

Views

The characteristic of real-closed fields is zero?

Published on 19 Jul 2015 - 7:22

score 65 · Answer 5 · 2015-07-19 15:49:11

65

Views

Field $F$ with $\operatorname{char}F=3$ and algebraic over $\mathbb{F}_3$ has a primitive root of unity.

Published on 19 Jul 2015 - 15:49

score 104 · Answer 6 · 2026-03-26 07:37:36

104

Views

Ordered fields are real?

Published on 26 Mar 2026 - 7:37

score 121 · Answer 7 · 2026-04-03 08:06:10

121

Views

Factoring ideals in algebraic number rings using Dedekind's theorem

Published on 03 Apr 2026 - 8:06

score 1.5k · Answer 8 · 2015-07-22 19:36:21

1.5k

Views

If $X^p-a$ has no zeros in a field $F$ of characteristic $p$ where $a \in F$, is it irreducible?

Published on 22 Jul 2015 - 19:36

score 47 · Answer 9 · 2015-07-23 08:42:08

47

Views

Choice of Primitive Element in ''Primitive Element Theorem''

Published on 23 Jul 2015 - 8:42

score 192 · Answer 10 · 2026-04-10 16:14:26

192

Views

A question about fields and separability in Serre's "Local Fields"

Published on 10 Apr 2026 - 16:14

score 236 · Answer 11 · 2026-04-12 03:04:46

236

Views

Can extension by an isomorphic field be of degree at least 2?

Published on 12 Apr 2026 - 3:04

score 55 · Answer 12 · 2015-08-02 11:25:18

Verify that $\sqrt{1+\sqrt2+\sqrt3+\sqrt5}$ is constructible by determining the sequence of its extension fields

score 191 · Answer 13 · 2026-04-11 15:47:24

191

Views

Galois group of maximally tamily ramified extension over the maximally unramified extension of a global function field F

Published on 11 Apr 2026 - 15:47

score 855 · Answer 14 · 2015-08-02 20:16:19

855

Views

Is $K := \mathbb{Q}(\cos (2\pi / 11))$ a Galois extension over $\mathbb{Q}$?

Published on 02 Aug 2015 - 20:16

score 206 · Answer 15 · 2026-03-25 19:32:48

206

Views

Cyclotomic extension of $K$, $Gal_{K}{F}$ is isomorphic to a subgroup of $\mathbb Z_n^*$

Published on 25 Mar 2026 - 19:32

List Question

Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$

$K/F$ Galois Extension, $H \leq G$, where $G$ the Galois group, then there is $\alpha \in K$ s.t. $H=\{\sigma \in G : \sigma \alpha = \alpha\}$.

Why the extension dimension of $x^3-2$ equal to $6$?

The characteristic of real-closed fields is zero?

Field $F$ with $\operatorname{char}F=3$ and algebraic over $\mathbb{F}_3$ has a primitive root of unity.

Ordered fields are real?

Factoring ideals in algebraic number rings using Dedekind's theorem

If $X^p-a$ has no zeros in a field $F$ of characteristic $p$ where $a \in F$, is it irreducible?

Choice of Primitive Element in ''Primitive Element Theorem''

A question about fields and separability in Serre's "Local Fields"

Can extension by an isomorphic field be of degree at least 2?

Verify that $\sqrt{1+\sqrt2+\sqrt3+\sqrt5}$ is constructible by determining the sequence of its extension fields

Galois group of maximally tamily ramified extension over the maximally unramified extension of a global function field F

Is $K := \mathbb{Q}(\cos (2\pi / 11))$ a Galois extension over $\mathbb{Q}$?

Cyclotomic extension of $K$, $Gal_{K}{F}$ is isomorphic to a subgroup of $\mathbb Z_n^*$

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