List questions from extension-field

Published on 12 Apr 2026 - 12:44

71

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Field extension contains no element in algebraic closure

Published on 14 Apr 2026 - 5:19

291

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Prime Degree Field Extension Separable

Published on 12 Apr 2026 - 15:49

83

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Characteristic infinite field

Published on 10 May 2026 - 22:30

89

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Constructing an isomorphism between $\mathbb{Q}(i,\sqrt{2})$ and $\mathbb{Q}(i + \sqrt{2})$

Published on 15 Apr 2026 - 14:07

1.4k

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If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Published on 14 Apr 2026 - 23:08

133

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Proof, that factor of irreducible polynomial is irreducible over field defined by root of irreducible

Published on 12 Apr 2026 - 3:10

186

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Square root in finite degree extension of odd characteristic field.

Published on 11 Apr 2026 - 0:37

1.3k

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Determine $[ \mathbb{Q} (\sqrt{2}, e^{2\pi i/3}) : \mathbb{Q}]$

Published on 16 Apr 2026 - 3:03

155

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confused about $\Bbb F_3(\alpha) \cong \Bbb F_3/\langle x^3+2x+2\rangle$

Published on 16 Apr 2026 - 5:51

169

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About number of algebra of dimension 2 over a field

Published on 14 Apr 2026 - 7:40

59

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Restrictions of $Gal(\mathbb{C}/\mathbb{Q})$ to a finite extension $\mathbb{K}$ of $\mathbb{Q}$

Published on 16 Apr 2026 - 3:02

269

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Calculate the square root of a number in $\mathbb{Q}(\sqrt[3]{7})$

Published on 16 Apr 2026 - 2:41

230

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Prove that $K \otimes_F F(\theta) \cong K[x]/(p(x))$ as $K$-algebras.

Published on 10 May 2026 - 11:21

2.2k

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Field and algebraic extension. How to prove that $[K: F]$ is finite?

Published on 13 Apr 2026 - 22:18

List Question

Why does the computation make sense?

Field extension contains no element in algebraic closure

Prime Degree Field Extension Separable

Characteristic infinite field

Constructing an isomorphism between $\mathbb{Q}(i,\sqrt{2})$ and $\mathbb{Q}(i + \sqrt{2})$

If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Proof, that factor of irreducible polynomial is irreducible over field defined by root of irreducible

Square root in finite degree extension of odd characteristic field.

Determine $[ \mathbb{Q} (\sqrt{2}, e^{2\pi i/3}) : \mathbb{Q}]$

confused about $\Bbb F_3(\alpha) \cong \Bbb F_3/\langle x^3+2x+2\rangle$

About number of algebra of dimension 2 over a field

Restrictions of $Gal(\mathbb{C}/\mathbb{Q})$ to a finite extension $\mathbb{K}$ of $\mathbb{Q}$

Calculate the square root of a number in $\mathbb{Q}(\sqrt[3]{7})$

Prove that $K \otimes_F F(\theta) \cong K[x]/(p(x))$ as $K$-algebras.

Field and algebraic extension. How to prove that $[K: F]$ is finite?

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