List questions from extension-field

Published on 03 Apr 2026 - 5:19

792

Views

For which prime numbers $p$ is $\cos(2\pi/p)$ irrational?

Published on 02 Apr 2026 - 5:25

26

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Show degree of a field extension over the rationals

Published on 27 Mar 2026 - 6:17

278

Views

Degree of field extension over the rationals

Published on 27 Mar 2026 - 6:17

126

Views

A degree $3$ extension of $\mathbb{C}(t)$

Published on 28 Mar 2017 - 1:02

676

Views

Finding one primitive element for splitting field of polynomial over $\mathbb{Q}$

Published on 27 Mar 2026 - 6:17

228

Views

how to determine Galois group of the $X^6-10X^3+1$ over rational field Q

Published on 30 Mar 2017 - 5:21

670

Views

Compute $[\mathbb{Q}(\pi):\mathbb{Q}(\pi^2)]$ and $\{\mathbb{Q}(\pi):\mathbb{Q}(\pi^2)\}$

Published on 27 Mar 2026 - 7:48

505

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How to find the irreducible polynomial in Q[ζ3]?

Published on 03 Apr 2026 - 5:18

237

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Dimension of an extension of a field

Published on 26 Mar 2026 - 17:47

48

Views

Can we write $-1$ as a sum of square in the splitting field of $x^4 + 4$ over $\Bbb{Q}$?

Published on 02 Apr 2017 - 4:47

128

Views

Let $\mathbb{K}$ be the splitting field of the polynomial $X^3 + X + 1$ over $\mathbb{Q}$

Published on 02 Apr 2017 - 4:56

343

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Subfield generated by 2 subfields

Published on 02 Apr 2017 - 12:24

165

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Degree $[\mathbb{Q}(α):\mathbb{Q}(α+α^{-1})]$

Published on 02 Apr 2017 - 16:32

592

Views

Galois Group of $\mathbb{Q}[\sqrt{3}, \sqrt{5}, \sqrt{7}]$

Published on 29 Mar 2026 - 5:50

List Question

Find the minimal polynomial of $i\sqrt{-1+2\sqrt3} \in \Bbb C$ over $\Bbb R$

For which prime numbers $p$ is $\cos(2\pi/p)$ irrational?

Show degree of a field extension over the rationals

Degree of field extension over the rationals

A degree $3$ extension of $\mathbb{C}(t)$

Finding one primitive element for splitting field of polynomial over $\mathbb{Q}$

how to determine Galois group of the $X^6-10X^3+1$ over rational field Q

Compute $[\mathbb{Q}(\pi):\mathbb{Q}(\pi^2)]$ and $\{\mathbb{Q}(\pi):\mathbb{Q}(\pi^2)\}$

How to find the irreducible polynomial in Q[ζ3]?

Dimension of an extension of a field

Can we write $-1$ as a sum of square in the splitting field of $x^4 + 4$ over $\Bbb{Q}$?

Let $\mathbb{K}$ be the splitting field of the polynomial $X^3 + X + 1$ over $\mathbb{Q}$

Subfield generated by 2 subfields

Degree $[\mathbb{Q}(α):\mathbb{Q}(α+α^{-1})]$

Galois Group of $\mathbb{Q}[\sqrt{3}, \sqrt{5}, \sqrt{7}]$

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