Question

A question about the embedding from $\mathbb{Q}(\sqrt{2},\sqrt{3})$ to an algebraic closure of $\mathbb{Q}$

score 51 · Answer 1 · 2026-05-15 14:16:59

51

Views

A question about the embedding from $\mathbb{Q}(\sqrt{2},\sqrt{3})$ to an algebraic closure of $\mathbb{Q}$

Published on 15 May 2026 - 14:16

score 35 · Answer 2 · 2026-04-11 13:15:48

35

Views

$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

Published on 11 Apr 2026 - 13:15

score 149 · Answer 3 · 2026-04-14 00:59:27

149

Views

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

Published on 14 Apr 2026 - 0:59

score 56 · Answer 4 · 2026-05-15 14:18:20

56

Views

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

Published on 15 May 2026 - 14:18

score 45 · Answer 5 · 2026-04-09 04:31:44

45

Views

Proving property of field trace

Published on 09 Apr 2026 - 4:31

score 50 · Answer 6 · 2026-04-14 18:16:53

50

Views

$K$ is the splitting field of degree $p$ polynomial $f(x)$. If $[K:F] =tp, t \in \mathbb{N}$, $f(x)$ is irreducible

Published on 14 Apr 2026 - 18:16

score 126 · Answer 7 · 2026-03-25 19:00:42

126

Views

Algebraic Structures involving (absorbing element).

Published on 25 Mar 2026 - 19:00

score 49 · Answer 8 · 2026-04-11 08:52:30

49

Views

Do we know all non-perfect fields?

Published on 11 Apr 2026 - 8:52

score 45 · Answer 9 · 2026-04-15 01:06:35

45

Views

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

Published on 15 Apr 2026 - 1:06

score 42 · Answer 10 · 2026-04-11 21:02:36

42

Views

Non commutative field of characteristic $\neq 0$

Published on 11 Apr 2026 - 21:02

score 42 · Answer 11 · 2026-04-17 08:12:27

42

Views

Find all field homomorphisms $f:\mathbb{Q}(\sqrt{2}) \rightarrow \mathbb{Q}(\sqrt{2})$

Published on 17 Apr 2026 - 8:12

score 39 · Answer 12 · 2026-04-13 18:46:32

39

Views

Degree of factors of the Artin–Schreier polynomial in $\mathbb{F}_q$.

Published on 13 Apr 2026 - 18:46

score 63 · Answer 13 · 2026-04-14 06:37:02

63

Views

Is every quasi-finite field algebraically closed?

Published on 14 Apr 2026 - 6:37

score 41 · Answer 14 · 2026-04-14 04:23:03

41

Views

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

Published on 14 Apr 2026 - 4:23

score 44 · Answer 15 · 2026-04-09 21:19:40

44

Views

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

Published on 09 Apr 2026 - 21:19

List Question

A question about the embedding from $\mathbb{Q}(\sqrt{2},\sqrt{3})$ to an algebraic closure of $\mathbb{Q}$

$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

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

Proving property of field trace

$K$ is the splitting field of degree $p$ polynomial $f(x)$. If $[K:F] =tp, t \in \mathbb{N}$, $f(x)$ is irreducible

Algebraic Structures involving (absorbing element).

Do we know all non-perfect fields?

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

Non commutative field of characteristic $\neq 0$

Find all field homomorphisms $f:\mathbb{Q}(\sqrt{2}) \rightarrow \mathbb{Q}(\sqrt{2})$

Degree of factors of the Artin–Schreier polynomial in $\mathbb{F}_q$.

Is every quasi-finite field algebraically closed?

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

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

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