List questions from galois-extensions

Published on 24 Oct 2018 - 2:26

407

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Closed points and rational points

Published on 24 Mar 2026 - 23:42

37

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Subfields of Galois Extensions and association with Galois Groups

Published on 25 Mar 2026 - 7:16

738

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M:K and L:K are normal and finite extensions then M intersection L : K is also finite and normal.

Published on 15 Nov 2018 - 20:41

855

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How to understand the Artin-Schreier correspondence?

Published on 25 Mar 2026 - 17:53

313

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There is an intermediate extension of degree $p$

Published on 19 Nov 2018 - 21:59

474

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Proving a subgroup of a Galois group is normal

Published on 27 Nov 2018 - 21:50

31

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Question about Galois group of a splitting field

Published on 29 Nov 2018 - 22:09

397

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Galois Field Matrix Multiplication for 512 bit number

Published on 01 Dec 2018 - 1:43

101

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Let $K = F_2(x)$ and $q_t(x) = x^2-x-t \in K[x]$. Show that $q_t$ is not solvable by radicals.

Published on 04 Dec 2018 - 2:53

901

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Describing the Galois group of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ without computing the extension degree (proof check please)

Published on 05 Dec 2018 - 11:52

512

Views

Proof with Galois theory that $K(\sqrt \alpha) = K(\sqrt \beta)$ if and only if it exists $\gamma$ with $\alpha = \gamma^2\beta$

Published on 13 Dec 2018 - 9:57

737

Views

Determine the fixed field of a field of rational functions and its Galois group.

Published on 14 Dec 2018 - 4:59

206

Views

Are the prime cyclotomic polynomials irreducible over any field where they're not obviously reducible ?

Published on 26 Mar 2026 - 6:34

55

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Weighted summation of irrational numbers

Published on 18 Dec 2018 - 1:47

List Question

Infinitely many number fields

Closed points and rational points

Subfields of Galois Extensions and association with Galois Groups

M:K and L:K are normal and finite extensions then M intersection L : K is also finite and normal.

How to understand the Artin-Schreier correspondence?

There is an intermediate extension of degree $p$

Proving a subgroup of a Galois group is normal

Question about Galois group of a splitting field

Galois Field Matrix Multiplication for 512 bit number

Let $K = F_2(x)$ and $q_t(x) = x^2-x-t \in K[x]$. Show that $q_t$ is not solvable by radicals.

Describing the Galois group of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ without computing the extension degree (proof check please)

Proof with Galois theory that $K(\sqrt \alpha) = K(\sqrt \beta)$ if and only if it exists $\gamma$ with $\alpha = \gamma^2\beta$

Determine the fixed field of a field of rational functions and its Galois group.

Are the prime cyclotomic polynomials irreducible over any field where they're not obviously reducible ?

Weighted summation of irrational numbers

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