Question

Compute how much overlap is needed

score 57 · Answer 1 · 2017-04-10 00:37:25

57

Views

Compute how much overlap is needed

Published on 10 Apr 2017 - 0:37

score 1.1k · Answer 2 · 2017-04-13 06:17:48

1.1k

Views

Composite of two Galois extensions

Published on 13 Apr 2017 - 6:17

score 92 · Answer 3 · 2017-04-14 21:36:20

92

Views

Splitting Field and Isomorphism of Field Extension

Published on 14 Apr 2017 - 21:36

score 82 · Answer 4 · 2017-04-20 15:16:48

82

Views

$[\mathbb{Q}(\sqrt{2})(\sqrt{6}) : \mathbb{Q}(\sqrt{3})]$ = ?.

Published on 20 Apr 2017 - 15:16

score 1.4k · Answer 5 · 2017-04-25 08:01:39

1.4k

Views

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

Published on 25 Apr 2017 - 8:01

score 944 · Answer 6 · 2026-03-27 13:42:14

944

Views

$f(x)$ irreducible over $\mathbb Q$ of prime degree ; then Galois group of $f$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f$?

Published on 27 Mar 2026 - 13:42

score 139 · Answer 7 · 2026-03-27 15:20:10

139

Views

$\operatorname{char} k=0$, $a,b,c,d,e \in k$ , then is the polynomial $f(x)=ax^8+bx^6+cx^4+dx^2+e$ solvable by radicals over $k$?

Published on 27 Mar 2026 - 15:20

score 496 · Answer 8 · 2026-03-27 15:18:57

496

Views

Quintic polynomial over rationals , with Galois group of order more than $24$ , is not solvable by radicals?

Published on 27 Mar 2026 - 15:18

score 541 · Answer 9 · 2017-04-26 22:59:45

541

Views

Prove that if $ x^p −1 $ splits completely, then $x^p−a $ for $a\in F$ is either irreducible or splits

Published on 26 Apr 2017 - 22:59

score 108 · Answer 10 · 2017-04-28 14:14:53

108

Views

$f(x) \in F[x]$ reducible,prime degree,for any extension $K/F$,if $f(x)$ has a root in $K$ then $f(x)$ splits in $K$,then $f(x)$ has a root in $F$?

Published on 28 Apr 2017 - 14:14

score 377 · Answer 11 · 2026-02-23 12:08:06

377

Views

Let $F\subseteq L\subseteq K$ be fields such that $K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal.

Published on 23 Feb 2026 - 12:08

score 90 · Answer 12 · 2017-05-12 22:25:13

90

Views

(From Milne's field theory notes)Why does the splitting field of a degree-$3$ irreduciblle polynomial has degree $3$ or $6$ over $\Bbb Q$?

Published on 12 May 2017 - 22:25

score 31 · Answer 13 · 2017-05-14 00:11:21

31

Views

Field extensions and irreducible polynomials

Published on 14 May 2017 - 0:11

score 201 · Answer 14 · 2017-05-16 19:45:00

201

Views

Find the degree of a splitting field.

Published on 16 May 2017 - 19:45

score 824 · Answer 15 · 2017-05-18 16:42:35

824

Views

Show that 2 splitting fields are isomoprhic.

Published on 18 May 2017 - 16:42

List Question

Compute how much overlap is needed

Composite of two Galois extensions

Splitting Field and Isomorphism of Field Extension

$[\mathbb{Q}(\sqrt{2})(\sqrt{6}) : \mathbb{Q}(\sqrt{3})]$ = ?.

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

$f(x)$ irreducible over $\mathbb Q$ of prime degree ; then Galois group of $f$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f$?

$\operatorname{char} k=0$, $a,b,c,d,e \in k$ , then is the polynomial $f(x)=ax^8+bx^6+cx^4+dx^2+e$ solvable by radicals over $k$?

Quintic polynomial over rationals , with Galois group of order more than $24$ , is not solvable by radicals?

Prove that if $ x^p −1 $ splits completely, then $x^p−a $ for $a\in F$ is either irreducible or splits

$f(x) \in F[x]$ reducible,prime degree,for any extension $K/F$,if $f(x)$ has a root in $K$ then $f(x)$ splits in $K$,then $f(x)$ has a root in $F$?

Let $F\subseteq L\subseteq K$ be fields such that $K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal.

(From Milne's field theory notes)Why does the splitting field of a degree-$3$ irreduciblle polynomial has degree $3$ or $6$ over $\Bbb Q$?

Field extensions and irreducible polynomials

Find the degree of a splitting field.

Show that 2 splitting fields are isomoprhic.

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