List questions from extension-field

Published on 17 Nov 2015 - 0:18

44

Views

If $K^{alg}$ is an algebraic closure of $K$ and $L$ is a field extension, does $K^{alg}$ also an algebraic closure of $L$?

Published on 17 Nov 2015 - 9:23

60

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Show that $K/\mathbb{Q}$ is Galois and find it's Galois group.

Published on 18 Nov 2015 - 2:25

23

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Prove the inclusions $G(L) ≤ G(E)$ and $F(H) ⊆ F(J)$

Published on 18 Nov 2015 - 3:37

455

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Show that two field extensions are equal

Published on 18 Nov 2015 - 3:40

68

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Element of $\text{Aut}_{\mathbb Q}(\mathbb Q(\sqrt[3]2),\mathbb Q^{alg})$.

Published on 18 Nov 2015 - 9:57

68

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Is $K[X]/(f)$ an algebraic extension?

Published on 18 Nov 2015 - 10:55

219

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Normal extension, why is $E/\mathbb F_p(t)$ normal?

Published on 06 Apr 2026 - 14:39

303

Views

Splitting field and field extension $\mathbb Q(j,\sqrt[3]2)$

Published on 28 Mar 2026 - 1:56

86

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Degree of $K(s)/K(s^n)$ and linear independence of powers of $s$.

Published on 19 Nov 2015 - 1:02

252

Views

Splitting $f(x)$ in $K_n$ Extension Field. What is the maximum degree of $K_n$

Published on 19 Nov 2015 - 5:15

772

Views

Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$

Published on 19 Nov 2015 - 17:57

100

Views

Finding all isomorphisms between two groups

Published on 04 Apr 2026 - 17:43

942

Views

Is every finitely generated field extension finite?

Published on 28 Mar 2026 - 1:46

1.8k

Views

If F/K is an algebraic field extension, is every endomorphism of F/K an automorphism?

Published on 22 Nov 2015 - 11:54

List Question

split $x^2+x+1$ in $z_2[x]/(x^2+x+1)$

If $K^{alg}$ is an algebraic closure of $K$ and $L$ is a field extension, does $K^{alg}$ also an algebraic closure of $L$?

Show that $K/\mathbb{Q}$ is Galois and find it's Galois group.

Prove the inclusions $G(L) ≤ G(E)$ and $F(H) ⊆ F(J)$

Show that two field extensions are equal

Element of $\text{Aut}_{\mathbb Q}(\mathbb Q(\sqrt[3]2),\mathbb Q^{alg})$.

Is $K[X]/(f)$ an algebraic extension?

Normal extension, why is $E/\mathbb F_p(t)$ normal?

Splitting field and field extension $\mathbb Q(j,\sqrt[3]2)$

Degree of $K(s)/K(s^n)$ and linear independence of powers of $s$.

Splitting $f(x)$ in $K_n$ Extension Field. What is the maximum degree of $K_n$

Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$

Finding all isomorphisms between two groups

Is every finitely generated field extension finite?

If F/K is an algebraic field extension, is every endomorphism of F/K an automorphism?

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