List questions from extension-field

Published on 14 Apr 2026 - 4:24

448

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Show that $α^2$ is algebraic over $K$

Published on 13 Apr 2026 - 2:47

1.2k

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What is an extension field? Covered differently in math & in cryptography.

Published on 12 Apr 2026 - 20:14

48

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Question about fields extension and induction.

Published on 13 Apr 2026 - 6:33

71

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Isomorphism between a polynomial field and $\mathbb{R}$

Published on 14 Apr 2026 - 14:48

49

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Confusion in Definition of separable polynomials

Published on 11 Apr 2026 - 3:32

272

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For $K/F$ be a separably generated field extension and for any finitely generated intermediate field $L$ $L/F$ is also separably generated.

Published on 15 Apr 2026 - 18:09

131

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Polynomial Ring of a Field extension

Published on 16 Apr 2026 - 1:05

83

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Finite field extension of $\mathbb{R}$, why must it admit an element such that $x^2+1=0$ Proof understanding.

Published on 11 Apr 2026 - 17:54

40

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Splitting field and monomorphism

Published on 12 Apr 2026 - 7:25

325

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Are the $n^\text{th}$ roots of an algebraic number algebraic?

Published on 12 Apr 2026 - 10:03

239

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Proving that $\left[ \mathbb{Q} \left( \sqrt[3]{4+\sqrt{5}} \right ) : \mathbb{Q} \right] = 6$

Published on 16 Apr 2026 - 22:47

60

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Question about field extension.

Published on 11 Apr 2026 - 3:54

1.1k

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Show $\mathbb{Q}( \sqrt{5},\sqrt{7} ) = \mathbb{Q}( \sqrt{5} + \sqrt{7} )$

Published on 17 Apr 2026 - 9:58

53

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Field with $\operatorname{char}K =p$.

Published on 13 Apr 2026 - 4:09

List Question

Sub-fields generated by algebraically independent set

Show that $α^2$ is algebraic over $K$

What is an extension field? Covered differently in math & in cryptography.

Question about fields extension and induction.

Isomorphism between a polynomial field and $\mathbb{R}$

Confusion in Definition of separable polynomials

For $K/F$ be a separably generated field extension and for any finitely generated intermediate field $L$ $L/F$ is also separably generated.

Polynomial Ring of a Field extension

Finite field extension of $\mathbb{R}$, why must it admit an element such that $x^2+1=0$ Proof understanding.

Splitting field and monomorphism

Are the $n^\text{th}$ roots of an algebraic number algebraic?

Proving that $\left[ \mathbb{Q} \left( \sqrt[3]{4+\sqrt{5}} \right ) : \mathbb{Q} \right] = 6$

Question about field extension.

Show $\mathbb{Q}( \sqrt{5},\sqrt{7} ) = \mathbb{Q}( \sqrt{5} + \sqrt{7} )$

Field with $\operatorname{char}K =p$.

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