List questions from extension-field

Published on 23 Mar 2018 - 17:01

68

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Field extension contains no element in algebraic closure

Published on 23 Mar 2018 - 17:18

288

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Prime Degree Field Extension Separable

Published on 23 Mar 2018 - 19:22

77

Views

Characteristic infinite field

Published on 24 Mar 2018 - 10:43

87

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

Published on 24 Mar 2018 - 13:41

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 24 Mar 2018 - 20:07

131

Views

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

Published on 25 Mar 2026 - 3:22

183

Views

Square root in finite degree extension of odd characteristic field.

Published on 26 Mar 2018 - 13:49

1.3k

Views

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

Published on 26 Mar 2018 - 22:47

152

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

Published on 27 Mar 2018 - 19:23

166

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About number of algebra of dimension 2 over a field

Published on 28 Mar 2018 - 3:23

56

Views

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

Published on 28 Mar 2018 - 12:14

267

Views

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

Published on 28 Mar 2018 - 14:19

226

Views

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

Published on 24 Mar 2026 - 22:07

2.2k

Views

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

Published on 29 Mar 2018 - 22:06

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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