Question

Step in the proof that for radical extension, its normal closure is also a radical extension

score 558 · Answer 1 · 2026-04-12 13:04:04

558

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Step in the proof that for radical extension, its normal closure is also a radical extension

Published on 12 Apr 2026 - 13:04

score 249 · Answer 2 · 2026-04-15 14:32:21

249

Views

Elemental proof of Zariski's lemma

Published on 15 Apr 2026 - 14:32

score 135 · Answer 3 · 2026-04-17 10:54:06

135

Views

If $[L_1:K] = p, [L_2:K] = q, \mbox { $p,q$ prime numbers}$, then $L_1\cap L_2 = K$ or $L_1=L_2$

Published on 17 Apr 2026 - 10:54

score 813 · Answer 4 · 2026-04-17 00:46:48

813

Views

$Gal(\mathbb{Q}(\sqrt[4]{2},i)/\mathbb{Q})$, choice of automorphisms

Published on 17 Apr 2026 - 0:46

score 1.2k · Answer 5 · 2026-04-15 11:49:29

1.2k

Views

$u$ and $v$ of degress relatively prime $m$ and $n$. Prove that $[F:K] = mn$

Published on 15 Apr 2026 - 11:49

score 1.1k · Answer 6 · 2026-04-14 16:06:54

1.1k

Views

Find the degree of $[F:\mathbb{Q}]$, where $F$ is the splitting field of $x^3-11$ over $\mathbb{Q}$

Published on 14 Apr 2026 - 16:06

score 1.1k · Answer 7 · 2026-03-25 23:42:14

1.1k

Views

Why is the degree of a rational map of projective curves equal to the degree of the homogeneous polynomials?

Published on 25 Mar 2026 - 23:42

score 68 · Answer 8 · 2026-04-15 04:36:15

68

Views

Is $e^{\pm 2\pi i/3}=1$ in the splitting field of $x^3-t\in \mathbb{F}_3(t)[x]$?

Published on 15 Apr 2026 - 4:36

score 80 · Answer 9 · 2026-04-12 05:17:38

80

Views

Product of polynomes in extensions

Published on 12 Apr 2026 - 5:17

score 651 · Answer 10 · 2026-04-16 13:09:19

651

Views

Find the degree of $\mathbb{Q}(i,\sqrt[4]{3}, \sqrt[6]{3})$ over $\mathbb{Q}$

Published on 16 Apr 2026 - 13:09

score 1k · Answer 11 · 2026-04-14 16:24:42

1k

Views

Galois of splitting field of $x^{12}-1$

Published on 14 Apr 2026 - 16:24

score 156 · Answer 12 · 2026-04-15 03:25:18

156

Views

Galois correspondence with the following field extensions

Published on 15 Apr 2026 - 3:25

score 479 · Answer 13 · 2026-04-11 15:00:43

479

Views

If $K$ is a field extension of $F$ and if $\alpha\in K$ is not separable over $F$, show that $\alpha^{p^m}$ is separable over $F$ for some

Published on 11 Apr 2026 - 15:00

score 229 · Answer 14 · 2026-04-13 05:23:30

229

Views

Commutative rings among whose proper subrings (with unity) , there exist a unique field

Published on 13 Apr 2026 - 5:23

score 41 · Answer 15 · 2026-04-10 18:08:20

41

Views

Purely complex degree four number field

Published on 10 Apr 2026 - 18:08

List Question

Step in the proof that for radical extension, its normal closure is also a radical extension

Elemental proof of Zariski's lemma

If $[L_1:K] = p, [L_2:K] = q, \mbox { $p,q$ prime numbers}$, then $L_1\cap L_2 = K$ or $L_1=L_2$

$Gal(\mathbb{Q}(\sqrt[4]{2},i)/\mathbb{Q})$, choice of automorphisms

$u$ and $v$ of degress relatively prime $m$ and $n$. Prove that $[F:K] = mn$

Find the degree of $[F:\mathbb{Q}]$, where $F$ is the splitting field of $x^3-11$ over $\mathbb{Q}$

Why is the degree of a rational map of projective curves equal to the degree of the homogeneous polynomials?

Is $e^{\pm 2\pi i/3}=1$ in the splitting field of $x^3-t\in \mathbb{F}_3(t)[x]$?

Product of polynomes in extensions

Find the degree of $\mathbb{Q}(i,\sqrt[4]{3}, \sqrt[6]{3})$ over $\mathbb{Q}$

Galois of splitting field of $x^{12}-1$

Galois correspondence with the following field extensions

If $K$ is a field extension of $F$ and if $\alpha\in K$ is not separable over $F$, show that $\alpha^{p^m}$ is separable over $F$ for some

Commutative rings among whose proper subrings (with unity) , there exist a unique field

Purely complex degree four number field

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