List questions from extension-field

Published on 12 Apr 2026 - 11:44

66

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Why $\mathbb{Q}(\sqrt{\alpha})\neq \mathbb{Q}(\sqrt{\beta})$ if $\sqrt{\alpha \beta} \notin \mathbb{Q}$?

Published on 17 Apr 2026 - 8:35

328

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Find units in $\mathbb{Z}[(\sqrt{13}+1)/2]$

Published on 16 Apr 2026 - 6:14

112

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Prove that $\mathbb{F}_2[X] / \left(x^3 + x + 1 \right)$ is a field with 8 elements

Published on 16 Apr 2026 - 18:52

318

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Prove $\operatorname{Gal}(EL/E)$ is a Galois extension in this case

Published on 14 Apr 2026 - 21:46

73

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Intermediate extensions are those corresponding to basis elements?

Published on 14 Apr 2026 - 10:50

96

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Splitting field of $X^3+X+1$ and $X^3-3$

Published on 14 Apr 2026 - 20:12

249

Views

Intermediate Galois extension of a simple radical extension in $\mathbb{R}$ has degree at most $2$

Published on 13 Apr 2026 - 16:54

54

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Is this a radical extension

Published on 10 Apr 2026 - 16:27

163

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How to prove whether $i\in\mathbb{Q}(\cos\frac{2\pi}{5}+i\sin\frac{2\pi}{5})$ or not

Published on 14 Apr 2026 - 10:33

212

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Is $\mathbb{Q}(\zeta + 1/\zeta)/\mathbb{Q}$ a radical extension?

Published on 15 Apr 2026 - 9:27

598

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show that $f(x)=x^3+x-6$ is irreducible over $\mathbb{Q}[i]$

Published on 15 Apr 2026 - 19:26

108

Views

Determine the splitting field

Published on 12 Apr 2026 - 4:21

356

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Showing that $[\mathbb{Q}(\sqrt[3]{2} \cdot \sqrt{3}) : \mathbb{Q}] = 6$

Published on 17 Apr 2026 - 11:09

103

Views

Does the separable degree equal the L.C.M.?

Published on 14 Apr 2026 - 16:04

List Question

What can be said about how an automorphism acts on the roots of a polynomial in $\mathbb{A}$

Why $\mathbb{Q}(\sqrt{\alpha})\neq \mathbb{Q}(\sqrt{\beta})$ if $\sqrt{\alpha \beta} \notin \mathbb{Q}$?

Find units in $\mathbb{Z}[(\sqrt{13}+1)/2]$

Prove that $\mathbb{F}_2[X] / \left(x^3 + x + 1 \right)$ is a field with 8 elements

Prove $\operatorname{Gal}(EL/E)$ is a Galois extension in this case

Intermediate extensions are those corresponding to basis elements?

Splitting field of $X^3+X+1$ and $X^3-3$

Intermediate Galois extension of a simple radical extension in $\mathbb{R}$ has degree at most $2$

Is this a radical extension

How to prove whether $i\in\mathbb{Q}(\cos\frac{2\pi}{5}+i\sin\frac{2\pi}{5})$ or not

Is $\mathbb{Q}(\zeta + 1/\zeta)/\mathbb{Q}$ a radical extension?

show that $f(x)=x^3+x-6$ is irreducible over $\mathbb{Q}[i]$

Determine the splitting field

Showing that $[\mathbb{Q}(\sqrt[3]{2} \cdot \sqrt{3}) : \mathbb{Q}] = 6$

Does the separable degree equal the L.C.M.?

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