List questions from extension-field

Published on 29 Oct 2023 - 9:44

32

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Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

Published on 27 Mar 2026 - 14:10

55

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Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Published on 27 Mar 2026 - 17:06

64

Views

Is $\mathbb{C}/\mathbb{Q}$ a simple field extension?

Published on 08 Nov 2023 - 9:47

108

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Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

Published on 27 Mar 2026 - 15:36

35

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Definition of simple radical extension.

Published on 06 Apr 2026 - 0:33

79

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Is there an example, such that $\omega\in F(\beta)\land \omega\notin F$?

Published on 26 Mar 2026 - 17:34

149

Views

Discriminant divisible by prime iff minimal polynomials reduction mod p has multiple roots

Published on 25 Mar 2026 - 17:19

45

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Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Published on 08 Apr 2026 - 9:51

23

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Dimension of a tensor product following field extension

Published on 18 Nov 2023 - 2:06

81

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Proving two field extensions aren't equal for different cube roots

Published on 20 Nov 2023 - 16:57

30

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Separable degree and extension degree

Published on 22 Nov 2023 - 14:52

29

Views

Extending an isomorphism between subfields of an algebraically closed field

Published on 30 Mar 2026 - 6:29

36

Views

Does $\max[E\cap F_i:E\cap F_{i-1}]\le\max[F_i:F_{i-1}]$ hold for $F_0\subset F_1\subset\cdots\subset F_n$ and $F_0\subset E\subset F_n$?

Published on 23 Nov 2023 - 20:44

82

Views

Factorization of polynomials in $\mathbb{Q_p}[X]$

Published on 26 Mar 2026 - 9:40

List Question

Extending a field isomorphism

Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Is $\mathbb{C}/\mathbb{Q}$ a simple field extension?

Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

Definition of simple radical extension.

Is there an example, such that $\omega\in F(\beta)\land \omega\notin F$?

Discriminant divisible by prime iff minimal polynomials reduction mod p has multiple roots

Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Dimension of a tensor product following field extension

Proving two field extensions aren't equal for different cube roots

Separable degree and extension degree

Extending an isomorphism between subfields of an algebraically closed field

Does $\max[E\cap F_i:E\cap F_{i-1}]\le\max[F_i:F_{i-1}]$ hold for $F_0\subset F_1\subset\cdots\subset F_n$ and $F_0\subset E\subset F_n$?

Factorization of polynomials in $\mathbb{Q_p}[X]$

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