Question

Field extension contains no element in algebraic closure

score 69 · Answer 1 · 2026-03-25 09:25:21

69

Views

Field extension contains no element in algebraic closure

Published on 25 Mar 2026 - 9:25

score 289 · Answer 2 · 2026-03-25 09:22:45

289

Views

Prime Degree Field Extension Separable

Published on 25 Mar 2026 - 9:22

score 46 · Answer 3 · 2026-03-26 22:29:55

46

Views

Finding intermediate fields and zeroes of a splitting field

Published on 26 Mar 2026 - 22:29

score 88 · Answer 4 · 2026-03-25 09:24:14

88

Views

Constructing an isomorphism between $\mathbb{Q}(i,\sqrt{2})$ and $\mathbb{Q}(i + \sqrt{2})$

Published on 25 Mar 2026 - 9:24

score 910 · Answer 5 · 2026-03-26 22:36:58

910

Views

Is $L$ normal over $E$ whenever it is normal over a subfield of $E$?

Published on 26 Mar 2026 - 22:36

score 1.4k · Answer 6 · 2026-03-25 09:30:02

1.4k

Views

If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Published on 25 Mar 2026 - 9:30

score 91 · Answer 7 · 2026-03-25 06:00:05

91

Views

Totally ordering the rationals with an injective function.

Published on 25 Mar 2026 - 6:00

score 79 · Answer 8 · 2026-03-22 09:38:00

79

Views

If $E/k$ is not separable, but satisfies the property that there exists a positive integer $n$ for which every $\alpha \in E$ of degree less than $n$

Published on 22 Mar 2026 - 9:38

score 476 · Answer 9 · 2026-03-26 22:33:33

476

Views

Suppose $Gal(K/Q)$ is the symmetric group $S_{n}$ with $n>2$. Show that if $n\geq 4$, then the $nth$ power of the roof of $f$ is not rational

Published on 26 Mar 2026 - 22:33

score 31 · Answer 10 · 2018-03-25 21:01:16

31

Views

Find the characteristic of the following field $F$.

Published on 25 Mar 2018 - 21:01

score 184 · Answer 11 · 2026-03-25 09:28:15

184

Views

Square root in finite degree extension of odd characteristic field.

Published on 25 Mar 2026 - 9:28

score 260 · Answer 12 · 2026-03-26 06:30:55

260

Views

Projective, free and semisimple submodules of $R =\left(\begin{smallmatrix} K & K \\ 0 & K \end{smallmatrix}\right)$

Published on 26 Mar 2026 - 6:30

score 1.3k · Answer 13 · 2026-03-25 09:24:04

1.3k

Views

Determine $[ \mathbb{Q} (\sqrt{2}, e^{2\pi i/3}) : \mathbb{Q}]$

Published on 25 Mar 2026 - 9:24

score 107 · Answer 14 · 2026-03-24 23:59:34

107

Views

Algebraic closure as directed colimit

Published on 24 Mar 2026 - 23:59

score 163 · Answer 15 · 2018-03-27 18:43:00

163

Views

showing that $F((t))=\big\{\sum\limits_{n=N}^{\infty}a_nt^n\ :\ N\in\mathbb{Z}, a_n\in F\big\}$ is a field for a field $F$

Published on 27 Mar 2018 - 18:43

List Question

Field extension contains no element in algebraic closure

Prime Degree Field Extension Separable

Finding intermediate fields and zeroes of a splitting field

Constructing an isomorphism between $\mathbb{Q}(i,\sqrt{2})$ and $\mathbb{Q}(i + \sqrt{2})$

Is $L$ normal over $E$ whenever it is normal over a subfield of $E$?

If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Totally ordering the rationals with an injective function.

If $E/k$ is not separable, but satisfies the property that there exists a positive integer $n$ for which every $\alpha \in E$ of degree less than $n$

Suppose $Gal(K/Q)$ is the symmetric group $S_{n}$ with $n>2$. Show that if $n\geq 4$, then the $nth$ power of the roof of $f$ is not rational

Find the characteristic of the following field $F$.

Square root in finite degree extension of odd characteristic field.

Projective, free and semisimple submodules of $R =\left(\begin{smallmatrix} K & K \\ 0 & K \end{smallmatrix}\right)$

Determine $[ \mathbb{Q} (\sqrt{2}, e^{2\pi i/3}) : \mathbb{Q}]$

Algebraic closure as directed colimit

showing that $F((t))=\big\{\sum\limits_{n=N}^{\infty}a_nt^n\ :\ N\in\mathbb{Z}, a_n\in F\big\}$ is a field for a field $F$

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