Question

Show that $(L : K), (Z : K)$ and $(L : Z)$ are all Galois extensions, but that $Z$ is not a stable intermediate field of $(L : K)$.

score 92 · Answer 1 · 2026-04-12 13:36:48

92

Views

Show that $(L : K), (Z : K)$ and $(L : Z)$ are all Galois extensions, but that $Z$ is not a stable intermediate field of $(L : K)$.

Published on 12 Apr 2026 - 13:36

score 214 · Answer 2 · 2026-04-16 06:25:25

214

Views

$(K(x) : F(U))$ is a Galois extension then $U$ is finite.

Published on 16 Apr 2026 - 6:25

score 580 · Answer 3 · 2026-04-12 09:14:51

580

Views

Is this equation solvable analytically?

Published on 12 Apr 2026 - 9:14

score 1.5k · Answer 4 · 2026-04-15 03:37:38

1.5k

Views

Distinguishing field extensions of $\mathbb{Q}$ of degree $3$.

Published on 15 Apr 2026 - 3:37

score 310 · Answer 5 · 2026-04-15 11:40:06

310

Views

Is there an algebraic extension $ F \neq \bar{\mathbf Q} $ of $ \mathbf Q $ such that every irreducible polynomial in $ F[X] $ has odd degree?

Published on 15 Apr 2026 - 11:40

score 64 · Answer 6 · 2026-04-16 11:35:43

64

Views

Show that $U = \langle\sigma\rangle$ is an infinite cyclic group; determine its fixed field $F(U)$ and the degree $[K(x) : F(U)]$.

Published on 16 Apr 2026 - 11:35

score 106 · Answer 7 · 2026-04-08 22:54:46

106

Views

fieldtheory questions

Published on 08 Apr 2026 - 22:54

score 57 · Answer 8 · 2026-04-14 01:10:27

57

Views

A question concerning finite extension field $E$ of perfect field $F$.

Published on 14 Apr 2026 - 1:10

score 317 · Answer 9 · 2026-04-15 09:03:56

317

Views

How to prove that a non-Archimedean ordered field implies that it doesn't have least upper bound property?

Published on 15 Apr 2026 - 9:03

score 75 · Answer 10 · 2026-04-17 05:35:48

75

Views

Show that $\mathbb Q(\sqrt[3]{2})[Y]/\langle Y^2+Y+1\rangle$ is a splitting field of $X^3-2$

Published on 17 Apr 2026 - 5:35

score 352 · Answer 11 · 2026-04-17 15:48:39

352

Views

Are there any rigid algebraically closed fields?

Published on 17 Apr 2026 - 15:48

score 467 · Answer 12 · 2026-04-16 09:51:37

467

Views

Splitting field of $x^3-11$ in $\Bbb Q$

Published on 16 Apr 2026 - 9:51

score 781 · Answer 13 · 2026-04-11 17:15:39

781

Views

Non-discrete valuation rings of Krull dimension 1

Published on 11 Apr 2026 - 17:15

score 91 · Answer 14 · 2026-04-11 23:10:56

91

Views

When does a polynomial remain irreducible when the fields are changed?

Published on 11 Apr 2026 - 23:10

score 68 · Answer 15 · 2026-04-16 04:09:53

68

Views

$E\otimes _FK$ is a simple ring or not?

Published on 16 Apr 2026 - 4:09

List Question

Show that $(L : K), (Z : K)$ and $(L : Z)$ are all Galois extensions, but that $Z$ is not a stable intermediate field of $(L : K)$.

$(K(x) : F(U))$ is a Galois extension then $U$ is finite.

Is this equation solvable analytically?

Distinguishing field extensions of $\mathbb{Q}$ of degree $3$.

Is there an algebraic extension $ F \neq \bar{\mathbf Q} $ of $ \mathbf Q $ such that every irreducible polynomial in $ F[X] $ has odd degree?

Show that $U = \langle\sigma\rangle$ is an infinite cyclic group; determine its fixed field $F(U)$ and the degree $[K(x) : F(U)]$.

fieldtheory questions

A question concerning finite extension field $E$ of perfect field $F$.

How to prove that a non-Archimedean ordered field implies that it doesn't have least upper bound property?

Show that $\mathbb Q(\sqrt[3]{2})[Y]/\langle Y^2+Y+1\rangle$ is a splitting field of $X^3-2$

Are there any rigid algebraically closed fields?

Splitting field of $x^3-11$ in $\Bbb Q$

Non-discrete valuation rings of Krull dimension 1

When does a polynomial remain irreducible when the fields are changed?

$E\otimes _FK$ is a simple ring or not?

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