List questions from extension-field

Published on 26 Mar 2026 - 17:46

75

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If $K(\zeta,\beta)/K$ is the splitting field for $f$, what can we say about $K(\zeta,\beta)/K(\zeta)$?

Published on 26 Mar 2026 - 17:47

101

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Non-normal and inseparable extension of degree 5

Published on 20 May 2020 - 11:53

299

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Finding a minimal polynomial of a root of unity over a field extension

Published on 30 Mar 2026 - 8:27

91

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Galois group of field extension

Published on 21 May 2020 - 6:22

123

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Why this polynomial reducible? (composite field)

Published on 28 Mar 2026 - 18:14

267

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Prime decomposition of pR in $\mathbb{A}\cap \mathbb{Q}[\alpha]$ for $\alpha={^3\sqrt{hk^2}}$ if p is a prime such that $p^2|m$

Published on 25 Mar 2026 - 11:54

40

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Degree of an exclusionary Field Extension

Published on 22 May 2020 - 19:49

1.3k

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Splitting field $L$ of polynomial $f \in K[x]$ with degree $n$ satisfies $[L:K] | n!$

Published on 26 Mar 2026 - 19:20

151

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Scalar restriction of bilinear maps

Published on 26 May 2020 - 18:13

88

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Representatives of residue classes as elements of a vector space

Published on 25 Mar 2026 - 9:26

54

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Find irreducible factors without factorizing

Published on 02 Apr 2026 - 7:51

37

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Why do we have $Q(\alpha, z) = \mathbb{Q}(\alpha, z, \overline{z})$ where $\alpha, z, \overline{z}$ are the roots of $X^3+X+1 \in \mathbb{Q}[x]$?

Published on 26 Mar 2026 - 19:19

95

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Multiplicative group of field extension over base field

Published on 28 May 2020 - 14:40

32

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Index of multiplicative group in field extension

Published on 28 May 2020 - 16:17

List Question

Find basis of $\mathbb Q(\sqrt[3]{2},\sqrt{-3})$ over the field $\mathbb Q(\sqrt[3]{2}\omega)$.

If $K(\zeta,\beta)/K$ is the splitting field for $f$, what can we say about $K(\zeta,\beta)/K(\zeta)$?

Non-normal and inseparable extension of degree 5

Finding a minimal polynomial of a root of unity over a field extension

Galois group of field extension

Why this polynomial reducible? (composite field)

Prime decomposition of pR in $\mathbb{A}\cap \mathbb{Q}[\alpha]$ for $\alpha={^3\sqrt{hk^2}}$ if p is a prime such that $p^2|m$

Degree of an exclusionary Field Extension

Splitting field $L$ of polynomial $f \in K[x]$ with degree $n$ satisfies $[L:K] | n!$

Scalar restriction of bilinear maps

Representatives of residue classes as elements of a vector space

Find irreducible factors without factorizing

Why do we have $Q(\alpha, z) = \mathbb{Q}(\alpha, z, \overline{z})$ where $\alpha, z, \overline{z}$ are the roots of $X^3+X+1 \in \mathbb{Q}[x]$?

Multiplicative group of field extension over base field

Index of multiplicative group in field extension

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