Question

How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?

score 60 · Answer 1 · 2022-07-30 22:50:45

60

Views

How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?

Published on 30 Jul 2022 - 22:50

score 53 · Answer 2 · 2026-03-27 23:48:09

53

Views

Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Published on 27 Mar 2026 - 23:48

score 37 · Answer 3 · 2022-07-31 15:55:53

37

Views

Show that $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely or doesnt over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))

Published on 31 Jul 2022 - 15:55

score 89 · Answer 4 · 2022-08-09 22:18:00

89

Views

Let $E$ be the splitting field of $f(x)=x^4-x^2-2$ over $\Bbb Q$. Find a basis for $E$.

Published on 09 Aug 2022 - 22:18

score 301 · Answer 5 · 2022-08-11 23:35:12

301

Views

Classification of degree $p$ field extensions of characteristic $p$ fields: the non-normal but separable case

Published on 11 Aug 2022 - 23:35

score 67 · Answer 6 · 2022-08-26 20:55:03

67

Views

Let $\mathbb F$ be a field of characteristic $p \gt 0$ and $a \in \mathbb F$ such that $a \ne b^p – b$ for all $b \in \mathbb F$

Published on 26 Aug 2022 - 20:55

score 154 · Answer 7 · 2022-08-29 19:57:13

154

Views

Show that there exists an $F$-isomorphism $\sigma : K \to K$ that takes $g$ to $h$

Published on 29 Aug 2022 - 19:57

score 38 · Answer 8 · 2026-03-26 17:53:46

38

Views

If E is a splitting field for A then it is clear that there exists a finitely generated subfield E'/F that is also a splitting field.

Published on 26 Mar 2026 - 17:53

score 210 · Answer 9 · 2026-03-30 20:55:33

210

Views

The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

Published on 30 Mar 2026 - 20:55

score 58 · Answer 10 · 2026-03-30 20:59:44

58

Views

The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Published on 30 Mar 2026 - 20:59

score 105 · Answer 11 · 2022-09-20 14:46:49

105

Views

Treating splitting fields as the same dangerous?

Published on 20 Sep 2022 - 14:46

score 163 · Answer 12 · 2026-03-30 20:52:39

163

Views

Finding Galois group of polynomial

Published on 30 Mar 2026 - 20:52

score 59 · Answer 13 · 2026-02-24 00:51:13

59

Views

Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

Published on 24 Feb 2026 - 0:51

score 40 · Answer 14 · 2022-10-08 10:38:50

40

Views

$L\to\overline{L}$ $K$-homomorphism restricts to an automorphism of L if L a splitting field of K

Published on 08 Oct 2022 - 10:38

score 96 · Answer 15 · 2026-02-24 00:49:33

96

Views

Infinite algebraic field extension of a finite field is normal and separable

Published on 24 Feb 2026 - 0:49

List Question

How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?

Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Show that $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely or doesnt over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))

Let $E$ be the splitting field of $f(x)=x^4-x^2-2$ over $\Bbb Q$. Find a basis for $E$.

Classification of degree $p$ field extensions of characteristic $p$ fields: the non-normal but separable case

Let $\mathbb F$ be a field of characteristic $p \gt 0$ and $a \in \mathbb F$ such that $a \ne b^p – b$ for all $b \in \mathbb F$

Show that there exists an $F$-isomorphism $\sigma : K \to K$ that takes $g$ to $h$

If E is a splitting field for A then it is clear that there exists a finitely generated subfield E'/F that is also a splitting field.

The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Treating splitting fields as the same dangerous?

Finding Galois group of polynomial

Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

$L\to\overline{L}$ $K$-homomorphism restricts to an automorphism of L if L a splitting field of K

Infinite algebraic field extension of a finite field is normal and separable

Trending Questions

Popular # Hahtags

Popular Questions