Question

Existence of certain autormorphism in Normal extensions

score 154 · Answer 1 · 2026-03-27 10:15:50

154

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Existence of certain autormorphism in Normal extensions

Published on 27 Mar 2026 - 10:15

score 399 · Answer 2 · 2026-03-25 11:21:26

399

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On the maximal unramified extension of $\mathbb{Q}_{p}$ of a given degree.

Published on 25 Mar 2026 - 11:21

score 69 · Answer 3 · 2026-03-25 16:20:54

69

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How to determine splitting field on $\mathbb{Q}$ of $f(X)= x^{15}-x^8-x^7+1$ and determine the degree over $\mathbb{Q}$

Published on 25 Mar 2026 - 16:20

score 246 · Answer 4 · 2026-03-27 16:19:21

246

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Infinitely many number fields

Published on 27 Mar 2026 - 16:19

score 255 · Answer 5 · 2026-03-29 18:13:32

255

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Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

Published on 29 Mar 2026 - 18:13

score 355 · Answer 6 · 2018-10-25 12:29:36

355

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If $L:K$ is a radical extension in $\mathbb {C}$, then the normal closure $M:K$ of $L:K$ is also radical.

Published on 25 Oct 2018 - 12:29

score 156 · Answer 7 · 2018-10-25 13:21:39

156

Views

Correct interpretation of solubility by radicals.

Published on 25 Oct 2018 - 13:21

score 101 · Answer 8 · 2026-03-29 18:15:22

101

Views

Give a direct proof that all elements of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ have the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}$

Published on 29 Mar 2026 - 18:15

score 117 · Answer 9 · 2018-10-26 19:40:02

117

Views

$P(P(a)) = a$. Are $a$ and $P(a)$ Galois conjugates?

Published on 26 Oct 2018 - 19:40

score 61 · Answer 10 · 2018-10-27 00:17:56

61

Views

Prove $L = F(β)$, where $β^p = F$ via Hilbert's Theorem 90

Published on 27 Oct 2018 - 0:17

score 32 · Answer 11 · 2018-10-27 00:50:36

32

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Show if $α ∈ L −$ {$0$} then $N(α) ∈ F − ${$0$}

Published on 27 Oct 2018 - 0:50

score 55 · Answer 12 · 2018-10-27 14:03:04

55

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Let $K$ be a subfield of $\mathbb {C}$ and let $L$ be the splitting field of $t^n-1$ over $K$. When is the Galois group of $L:K$ abelian?

Published on 27 Oct 2018 - 14:03

score 60 · Answer 13 · 2026-03-25 17:52:10

60

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Proving irreducibiltity of $f(X)=X^3 -2 \in \mathbb{Q}[X]$ at $ \mathbb{Q}(\sqrt{2})$

Published on 25 Mar 2026 - 17:52

score 323 · Answer 14 · 2026-03-26 02:57:48

323

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An easy trick to compute the Galois group of a product of high degree polynomials

Published on 26 Mar 2026 - 2:57

score 334 · Answer 15 · 2026-03-25 03:23:00

334

Views

Algebraic 1-cocycles and Galois gerbs

Published on 25 Mar 2026 - 3:23

List Question

Existence of certain autormorphism in Normal extensions

On the maximal unramified extension of $\mathbb{Q}_{p}$ of a given degree.

How to determine splitting field on $\mathbb{Q}$ of $f(X)= x^{15}-x^8-x^7+1$ and determine the degree over $\mathbb{Q}$

Infinitely many number fields

Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

If $L:K$ is a radical extension in $\mathbb {C}$, then the normal closure $M:K$ of $L:K$ is also radical.

Correct interpretation of solubility by radicals.

Give a direct proof that all elements of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ have the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}$

$P(P(a)) = a$. Are $a$ and $P(a)$ Galois conjugates?

Prove $L = F(β)$, where $β^p = F$ via Hilbert's Theorem 90

Show if $α ∈ L −$ {$0$} then $N(α) ∈ F − ${$0$}

Let $K$ be a subfield of $\mathbb {C}$ and let $L$ be the splitting field of $t^n-1$ over $K$. When is the Galois group of $L:K$ abelian?

Proving irreducibiltity of $f(X)=X^3 -2 \in \mathbb{Q}[X]$ at $ \mathbb{Q}(\sqrt{2})$

An easy trick to compute the Galois group of a product of high degree polynomials

Algebraic 1-cocycles and Galois gerbs

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