Question

Show that a finite Galois extension has a finite number of intermediate fields.

score 109 · Answer 1 · 2026-04-15 07:21:37

109

Views

Show that a finite Galois extension has a finite number of intermediate fields.

Published on 15 Apr 2026 - 7:21

score 27 · Answer 2 · 2026-04-12 17:22:14

27

Views

Solving equation for a field extension

Published on 12 Apr 2026 - 17:22

score 36 · Answer 3 · 2026-04-12 05:27:30

36

Views

Intersection of Galois extensions with additional algebraic element.

Published on 12 Apr 2026 - 5:27

score 118 · Answer 4 · 2026-04-14 20:52:04

118

Views

Show set of matrices forms a finite field of order 27

Published on 14 Apr 2026 - 20:52

score 107 · Answer 5 · 2026-03-28 12:58:44

107

Views

Which of the following pairs is an extension of fields?

Published on 28 Mar 2026 - 12:58

score 195 · Answer 6 · 2026-03-25 17:22:43

195

Views

Dieudonné module of the constant group scheme $\mathbb Z/p^n\mathbb Z$

Published on 25 Mar 2026 - 17:22

score 38 · Answer 7 · 2026-04-11 12:15:13

38

Views

Condition for every faithful module to be free

Published on 11 Apr 2026 - 12:15

score 49 · Answer 8 · 2026-04-17 12:32:41

49

Views

$\frac{f(X)}{g(X)} = \frac{f(-X)}{g(-X)} ∈ ℚ(X)$

Published on 17 Apr 2026 - 12:32

score 259 · Answer 9 · 2026-04-16 23:04:31

259

Views

There are infinitely many non-isomorphic cubic Galois extension of $\mathbb Q$

Published on 16 Apr 2026 - 23:04

score 61 · Answer 10 · 2026-04-11 07:23:20

61

Views

Is an element separable over two fields separable over their intersection?

Published on 11 Apr 2026 - 7:23

score 70 · Answer 11 · 2026-03-26 14:22:41

70

Views

Number of Abelian Cubic Number Fields of given Discriminant

Published on 26 Mar 2026 - 14:22

score 262 · Answer 12 · 2026-04-15 07:24:49

262

Views

If every irreducible polynomial in $K[x]$ is separable then every algebraic closure $\bar{K}$ of $K$ is Galois over $K$?

Published on 15 Apr 2026 - 7:24

score 56 · Answer 13 · 2026-04-15 13:56:54

56

Views

Proving every algebraically independent subset of $F$ is contained in a transcendence basis.

Published on 15 Apr 2026 - 13:56

score 28 · Answer 14 · 2026-04-14 18:40:13

28

Views

A result when $G(K,F)\cong S_3$

Published on 14 Apr 2026 - 18:40

score 70 · Answer 15 · 2026-04-10 09:15:33

70

Views

Why is $x-\zeta^a$ a linear factor if $x-\zeta^p$ is a linear factor of a polynomial?

Published on 10 Apr 2026 - 9:15

List Question

Show that a finite Galois extension has a finite number of intermediate fields.

Solving equation for a field extension

Intersection of Galois extensions with additional algebraic element.

Show set of matrices forms a finite field of order 27

Which of the following pairs is an extension of fields?

Dieudonné module of the constant group scheme $\mathbb Z/p^n\mathbb Z$

Condition for every faithful module to be free

$\frac{f(X)}{g(X)} = \frac{f(-X)}{g(-X)} ∈ ℚ(X)$

There are infinitely many non-isomorphic cubic Galois extension of $\mathbb Q$

Is an element separable over two fields separable over their intersection?

Number of Abelian Cubic Number Fields of given Discriminant

If every irreducible polynomial in $K[x]$ is separable then every algebraic closure $\bar{K}$ of $K$ is Galois over $K$?

Proving every algebraically independent subset of $F$ is contained in a transcendence basis.

A result when $G(K,F)\cong S_3$

Why is $x-\zeta^a$ a linear factor if $x-\zeta^p$ is a linear factor of a polynomial?

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