Question

If $K$ is a field of characteristic $0$ in which every polynomial of degree $\geq3$ is reducible, then $\bar{K}/K$ has degree $1$ or $2$

score 39 · Answer 1 · 2024-03-05 19:01:47

39

Views

If $K$ is a field of characteristic $0$ in which every polynomial of degree $\geq3$ is reducible, then $\bar{K}/K$ has degree $1$ or $2$

Published on 05 Mar 2024 - 19:01

score 37 · Answer 2 · 2026-04-06 20:33:14

37

Views

Prove that $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ iff $m$ divides $n$

Published on 06 Apr 2026 - 20:33

score 75 · Answer 3 · 2026-03-27 18:39:47

75

Views

Arguments for Galois closure of $\mathbb{Q}(\sqrt[3]{2})$

Published on 27 Mar 2026 - 18:39

score 56 · Answer 4 · 2024-03-08 11:23:51

56

Views

$F_1\subset F_2\implies [F_2(\alpha):F_2]\leq [F_1(\alpha):F_1]$

Published on 08 Mar 2024 - 11:23

score 147 · Answer 5 · 2024-03-08 20:15:56

147

Views

How many solutions can $x^4=-1$ have on a field of characteristic $0$?

Published on 08 Mar 2024 - 20:15

score 53 · Answer 6 · 2026-03-29 12:39:21

53

Views

Some questions about the trace of $\alpha \in K$ from $K$ to $F$ where $K,F$ are fields

Published on 29 Mar 2026 - 12:39

score 48 · Answer 7 · 2026-02-23 12:00:25

48

Views

Do we know all non-perfect fields?

Published on 23 Feb 2026 - 12:00

score 42 · Answer 8 · 2024-03-12 11:47:42

42

Views

A question about the degree of field extension $[\mathbb{Q}(\sqrt[p]{2},\zeta) : \mathbb{Q}]$

Published on 12 Mar 2024 - 11:47

score 39 · Answer 9 · 2026-03-28 20:56:00

39

Views

A question about how to represent $\mathbb{Q}(\zeta_n)$ differently

Published on 28 Mar 2026 - 20:56

score 43 · Answer 10 · 2026-02-23 12:07:12

43

Views

Showing that any two separable closures of a field are $K$-isomorphic

Published on 23 Feb 2026 - 12:07

score 59 · Answer 11 · 2026-02-23 02:40:44

59

Views

Transcendence degree of $F(x)$ over a field $F$

Published on 23 Feb 2026 - 2:40

score 42 · Answer 12 · 2026-04-08 00:43:41

42

Views

Example of non isomorphic field extensions

Published on 08 Apr 2026 - 0:43

score 24 · Answer 13 · 2026-03-27 17:06:30

24

Views

Normal closure of $\mathbb{Q}(\sqrt{2 + \sqrt{2}})/\mathbb{Q}$

Published on 27 Mar 2026 - 17:06

score 26 · Answer 14 · 2026-02-23 12:09:14

26

Views

Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Published on 23 Feb 2026 - 12:09

score 106 · Answer 15 · 2026-04-06 22:13:54

106

Views

Why $[\mathbb{F}_{p}(\alpha): \mathbb{F}_{p^n}] = p$?

Published on 06 Apr 2026 - 22:13

List Question

If $K$ is a field of characteristic $0$ in which every polynomial of degree $\geq3$ is reducible, then $\bar{K}/K$ has degree $1$ or $2$

Prove that $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ iff $m$ divides $n$

Arguments for Galois closure of $\mathbb{Q}(\sqrt[3]{2})$

$F_1\subset F_2\implies [F_2(\alpha):F_2]\leq [F_1(\alpha):F_1]$

How many solutions can $x^4=-1$ have on a field of characteristic $0$?

Some questions about the trace of $\alpha \in K$ from $K$ to $F$ where $K,F$ are fields

Do we know all non-perfect fields?

A question about the degree of field extension $[\mathbb{Q}(\sqrt[p]{2},\zeta) : \mathbb{Q}]$

A question about how to represent $\mathbb{Q}(\zeta_n)$ differently

Showing that any two separable closures of a field are $K$-isomorphic

Transcendence degree of $F(x)$ over a field $F$

Example of non isomorphic field extensions

Normal closure of $\mathbb{Q}(\sqrt{2 + \sqrt{2}})/\mathbb{Q}$

Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Why $[\mathbb{F}_{p}(\alpha): \mathbb{F}_{p^n}] = p$?

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