List questions from extension-field

Published on 28 Apr 2018 - 2:11

73

Views

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

Published on 28 Apr 2018 - 22:06

103

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

Published on 28 Apr 2018 - 22:14

58

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Automorphism on finitely generated field.

Published on 29 Apr 2018 - 1:15

1.1k

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Galois extensions over $\mathbb{Q}$.

Published on 29 Apr 2018 - 2:36

61

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

Published on 29 Apr 2018 - 21:42

28

Views

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

Published on 30 Apr 2018 - 0:21

195

Views

Are normal extensions always simple?

Published on 22 Mar 2026 - 23:20

91

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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 30 Apr 2018 - 2:21

178

Views

On Galois intersection

Published on 30 Apr 2018 - 8:55

66

Views

Set generated by all finite field operations.

Published on 30 Apr 2018 - 17:47

70

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How to make a field extension chain

Published on 30 Apr 2018 - 19:10

177

Views

Galois Theory. Fixed Field. Find the minimal polynomial.

Published on 01 May 2018 - 3:24

183

Views

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

Published on 01 May 2018 - 3:28

407

Views

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

Published on 02 May 2018 - 3:24

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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