Question

Algebraic closure of completions in function fields

score 65 · Answer 1 · 2026-03-25 01:26:00

65

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Algebraic closure of completions in function fields

Published on 25 Mar 2026 - 1:26

score 204 · Answer 2 · 2026-04-15 19:37:43

204

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How to show that $x^9-3$ is irreducible over $\mathbb Q\Big(\exp\left(\frac{2\pi i}5\right)\Big)$?

Published on 15 Apr 2026 - 19:37

score 206 · Answer 3 · 2026-04-17 16:04:34

206

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Prove $x^{p^k}-a$ is irreducible in a field $K$ of characteristic $p>0$ for all $k \geq 0$, where $a$ is not a $p^{th}$ power in $K$.

Published on 17 Apr 2026 - 16:04

score 1.6k · Answer 4 · 2026-04-14 04:16:55

1.6k

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Dividing an angle into five equal parts by ruler and Compass Construction

Published on 14 Apr 2026 - 4:16

score 176 · Answer 5 · 2026-04-12 23:41:03

176

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$C$ has an extension of degree $p$ if and only if $p\neq2$. Where $C$ is the field of all constructible real numbers

Published on 12 Apr 2026 - 23:41

score 118 · Answer 6 · 2026-04-17 08:20:32

118

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Fréchet derivative of a operator $E: H_{per}^{1}\left([0,L]\right) \longrightarrow \mathbb{R}$

Published on 17 Apr 2026 - 8:20

score 752 · Answer 7 · 2026-04-14 07:10:00

752

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Let $K$ be a field containing an integral domain $D$ and $F$ be the field of quotients of $D$. Then $K$ contains a field isomorphic to $F$.

Published on 14 Apr 2026 - 7:10

score 52 · Answer 8 · 2026-04-12 09:57:13

52

Views

About minimal polynomial of an $p$th root (Field extension whose characteristic is $p$)

Published on 12 Apr 2026 - 9:57

score 45 · Answer 9 · 2026-04-13 23:20:09

45

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Understanding proof of proposition $x \in F \to x \cdot 0 = 0$ where $F$ is a field.

Published on 13 Apr 2026 - 23:20

score 127 · Answer 10 · 2026-03-29 13:40:46

127

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Automorphism group of $F$, where $F$ is the quotient field of the integral domain $R=\Bbb Z[x]/(x^3+x+1)$

Published on 29 Mar 2026 - 13:40

score 24 · Answer 11 · 2026-04-04 15:06:48

24

Views

Degree of field extension using minimal polynomials

Published on 04 Apr 2026 - 15:06

score 490 · Answer 12 · 2026-04-15 05:36:40

490

Views

Let $f$ be an irreducible cubic polynomial over $\mathbb Q$ with exactly one real root and $K$ the splitting field of $f$.

Published on 15 Apr 2026 - 5:36

score 698 · Answer 13 · 2026-04-12 22:57:14

698

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Show that the degree of any finite extension of $F$ is a power of $p$

Published on 12 Apr 2026 - 22:57

score 69 · Answer 14 · 2026-04-16 03:21:37

69

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I can't understand why the elements \alpha_i\beta_j spans the field K_1K_2, Abstract Algebra by Dummit and Foote p.528

Published on 16 Apr 2026 - 3:21

score 45 · Answer 15 · 2026-04-11 20:40:33

45

Views

Working out the structure of a finitely generated field

Published on 11 Apr 2026 - 20:40

List Question

Algebraic closure of completions in function fields

How to show that $x^9-3$ is irreducible over $\mathbb Q\Big(\exp\left(\frac{2\pi i}5\right)\Big)$?

Prove $x^{p^k}-a$ is irreducible in a field $K$ of characteristic $p>0$ for all $k \geq 0$, where $a$ is not a $p^{th}$ power in $K$.

Dividing an angle into five equal parts by ruler and Compass Construction

$C$ has an extension of degree $p$ if and only if $p\neq2$. Where $C$ is the field of all constructible real numbers

Fréchet derivative of a operator $E: H_{per}^{1}\left([0,L]\right) \longrightarrow \mathbb{R}$

Let $K$ be a field containing an integral domain $D$ and $F$ be the field of quotients of $D$. Then $K$ contains a field isomorphic to $F$.

About minimal polynomial of an $p$th root (Field extension whose characteristic is $p$)

Understanding proof of proposition $x \in F \to x \cdot 0 = 0$ where $F$ is a field.

Automorphism group of $F$, where $F$ is the quotient field of the integral domain $R=\Bbb Z[x]/(x^3+x+1)$

Degree of field extension using minimal polynomials

Let $f$ be an irreducible cubic polynomial over $\mathbb Q$ with exactly one real root and $K$ the splitting field of $f$.

Show that the degree of any finite extension of $F$ is a power of $p$

I can't understand why the elements \alpha_i\beta_j spans the field K_1K_2, Abstract Algebra by Dummit and Foote p.528

Working out the structure of a finitely generated field

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