List questions from extension-field

Published on 09 Apr 2026 - 20:51

76

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Show that the $\mathbb{Q}$-homomorphism is well-defined.

Published on 14 Apr 2026 - 3:23

106

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Exercise on degree extensions of quadratic subfield over $\Bbb Q$

Published on 13 Apr 2026 - 20:56

61

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Automorphism on finitely generated field.

Published on 10 Apr 2026 - 19:14

1.1k

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Galois extensions over $\mathbb{Q}$.

Published on 12 Apr 2026 - 9:00

64

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The degree extension $Q(\sqrt{2},\sqrt[3]{2},\sqrt[4]{2})$

Published on 15 Apr 2026 - 19:52

31

Views

If $F(a) \subseteq F(c)$, then $F(c)$ is an extension of $F(a)$

Published on 14 Apr 2026 - 8:45

201

Views

Are normal extensions always simple?

Published on 10 May 2026 - 15:20

94

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Show that if A is algebraic closure of F and K is an intermediate field, then A is also the algebraic closure of K. Confirm solution?

Published on 14 Apr 2026 - 22:26

180

Views

On Galois intersection

Published on 13 Apr 2026 - 10:13

68

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Set generated by all finite field operations.

Published on 13 Apr 2026 - 5:32

73

Views

How to make a field extension chain

Published on 12 Apr 2026 - 11:31

180

Views

Galois Theory. Fixed Field. Find the minimal polynomial.

Published on 12 Apr 2026 - 0:05

186

Views

Hint needed for Galois theory for a quartic without using the discriminant

Published on 10 Apr 2026 - 10:58

410

Views

What is the Galois Group of $f(t)=t^6-2t^3-1$ over $K:=\mathbb{Q}$?

Published on 15 Apr 2026 - 15:32

List Question

Galois Theory and automorphisms

Show that the $\mathbb{Q}$-homomorphism is well-defined.

Exercise on degree extensions of quadratic subfield over $\Bbb Q$

Automorphism on finitely generated field.

Galois extensions over $\mathbb{Q}$.

The degree extension $Q(\sqrt{2},\sqrt[3]{2},\sqrt[4]{2})$

If $F(a) \subseteq F(c)$, then $F(c)$ is an extension of $F(a)$

Are normal extensions always simple?

Show that if A is algebraic closure of F and K is an intermediate field, then A is also the algebraic closure of K. Confirm solution?

On Galois intersection

Set generated by all finite field operations.

How to make a field extension chain

Galois Theory. Fixed Field. Find the minimal polynomial.

Hint needed for Galois theory for a quartic without using the discriminant

What is the Galois Group of $f(t)=t^6-2t^3-1$ over $K:=\mathbb{Q}$?

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