Question

Fields of characteristic $p$ where there exists an element $a$ that is not a p:th power.

score 59 · Answer 1 · 2026-04-17 15:09:45

59

Views

Fields of characteristic $p$ where there exists an element $a$ that is not a p:th power.

Published on 17 Apr 2026 - 15:09

score 36 · Answer 2 · 2026-04-29 23:02:45

36

Views

Correcting the map that proves countability of $N.$

Published on 29 Apr 2026 - 23:02

score 53 · Answer 3 · 2026-04-17 04:00:33

53

Views

For any prime $p$ and any non-zero $a \in \mathbb{F}_p$, prove that $p(x) = x^p-x+a$ is irreducible and seperable.

Published on 17 Apr 2026 - 4:00

score 56 · Answer 4 · 2026-04-14 20:22:25

56

Views

Constructing the algebraic closure of $\mathbb{F}_{p}$

Published on 14 Apr 2026 - 20:22

score 84 · Answer 5 · 2026-04-12 17:55:25

84

Views

Proving two field extensions aren't equal for different cube roots

Published on 12 Apr 2026 - 17:55

score 41 · Answer 6 · 2026-04-14 21:32:26

41

Views

Showing that $\text{Gal}(L|EF) = \text{Gal}(L|E) \cap \text{Gal}(L|F)$

Published on 14 Apr 2026 - 21:32

score 33 · Answer 7 · 2026-04-13 22:44:26

33

Views

Separable degree and extension degree

Published on 13 Apr 2026 - 22:44

score 31 · Answer 8 · 2026-04-14 02:21:33

31

Views

Extending an isomorphism between subfields of an algebraically closed field

Published on 14 Apr 2026 - 2:21

score 38 · Answer 9 · 2026-04-16 06:41:05

38

Views

Does $\max[E\cap F_i:E\cap F_{i-1}]\le\max[F_i:F_{i-1}]$ hold for $F_0\subset F_1\subset\cdots\subset F_n$ and $F_0\subset E\subset F_n$?

Published on 16 Apr 2026 - 6:41

score 101 · Answer 10 · 2026-05-14 16:03:43

101

Views

Why do we fix an extension of valuation of $K$ to $\overline{K}$?

Published on 14 May 2026 - 16:03

score 35 · Answer 11 · 2026-04-15 19:14:46

35

Views

Given $F_0\subset\cdots\subset F_n$ and intermediate $E$, finding $F=E_0\subset\cdots\subset E_m=E$ such that $\max[E_i:E_{i-1}]\le\max[F_i:F_{i-1}]$

Published on 15 Apr 2026 - 19:14

score 41 · Answer 12 · 2026-04-12 22:03:02

41

Views

Ordering of $\mathbb{R}[X]$ such that $0 < X < a$ for all positive numbers $a$

Published on 12 Apr 2026 - 22:03

score 72 · Answer 13 · 2026-04-15 10:54:54

72

Views

Show that $N_G(C)$ is just subgroup $H$.

Published on 15 Apr 2026 - 10:54

score 167 · Answer 14 · 2026-05-14 08:32:33

167

Views

A natural topology on a field

Published on 14 May 2026 - 8:32

score 119 · Answer 15 · 2026-04-14 11:59:48

119

Views

Topology induced by generalised absolute values

Published on 14 Apr 2026 - 11:59

List Question

Fields of characteristic $p$ where there exists an element $a$ that is not a p:th power.

Correcting the map that proves countability of $N.$

For any prime $p$ and any non-zero $a \in \mathbb{F}_p$, prove that $p(x) = x^p-x+a$ is irreducible and seperable.

Constructing the algebraic closure of $\mathbb{F}_{p}$

Proving two field extensions aren't equal for different cube roots

Showing that $\text{Gal}(L|EF) = \text{Gal}(L|E) \cap \text{Gal}(L|F)$

Separable degree and extension degree

Extending an isomorphism between subfields of an algebraically closed field

Does $\max[E\cap F_i:E\cap F_{i-1}]\le\max[F_i:F_{i-1}]$ hold for $F_0\subset F_1\subset\cdots\subset F_n$ and $F_0\subset E\subset F_n$?

Why do we fix an extension of valuation of $K$ to $\overline{K}$?

Given $F_0\subset\cdots\subset F_n$ and intermediate $E$, finding $F=E_0\subset\cdots\subset E_m=E$ such that $\max[E_i:E_{i-1}]\le\max[F_i:F_{i-1}]$

Ordering of $\mathbb{R}[X]$ such that $0 < X < a$ for all positive numbers $a$

Show that $N_G(C)$ is just subgroup $H$.

A natural topology on a field

Topology induced by generalised absolute values

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