Question

Suppose char$(F) = p$ and $E/F$ with $[E:F] = p$. Then if there is one inseparable element then every element in $E\setminus F$ is inseparable

score 56 · Answer 1 · 2026-04-17 14:03:04

56

Views

Suppose char$(F) = p$ and $E/F$ with $[E:F] = p$. Then if there is one inseparable element then every element in $E\setminus F$ is inseparable

Published on 17 Apr 2026 - 14:03

score 53 · Answer 2 · 2026-04-17 11:30:55

53

Views

If $G=\mathsf{Aut}_k(F)$ acts on field $F$ algebraic over $k$ then do we have: orbit $G\alpha=\text{ roots of minimal polynomial of }\alpha$?

Published on 17 Apr 2026 - 11:30

score 196 · Answer 3 · 2026-04-15 15:07:32

196

Views

Is there a quadratically closed field strictly between the quadratic closures of $\mathbb{Q}$ and $\mathbb{Q}(\sqrt[3]{2})$?

Published on 15 Apr 2026 - 15:07

score 72 · Answer 4 · 2026-04-17 01:12:41

72

Views

Number of roots of irreducible polynomials in extension fields

Published on 17 Apr 2026 - 1:12

score 162 · Answer 5 · 2026-04-16 02:15:52

162

Views

show that $x\in E$ is transcendental over $F$

Published on 16 Apr 2026 - 2:15

score 436 · Answer 6 · 2026-04-09 04:50:13

436

Views

Frobenius-endomorphism surjective $\Rightarrow$ field perfect

Published on 09 Apr 2026 - 4:50

score 120 · Answer 7 · 2026-04-16 20:34:37

120

Views

Let $K=\mathbb{Q}(i), L=K(\sqrt[3]{3+i}), M=K(\sqrt{\pi}/2)$. Find all $K$-automorphisms of $L$ and $M$.

Published on 16 Apr 2026 - 20:34

score 110 · Answer 8 · 2026-04-13 23:50:33

110

Views

Existence of irreducible Polynomials in finite fields

Published on 13 Apr 2026 - 23:50

score 64 · Answer 9 · 2026-04-11 08:16:43

64

Views

What is the Galois group of this extension?

Published on 11 Apr 2026 - 8:16

score 98 · Answer 10 · 2026-04-14 09:56:41

98

Views

Show that this extension of function fields over $\mathbb{F}_{81}$ is normal

Published on 14 Apr 2026 - 9:56

score 104 · Answer 11 · 2026-04-16 05:15:03

104

Views

On normal extension, a square root of discriminant is in field F?

Published on 16 Apr 2026 - 5:15

score 88 · Answer 12 · 2026-04-16 12:05:02

88

Views

About the primitive elements of $\mathbb{Q}(\sqrt{3},i\sqrt{5})$

Published on 16 Apr 2026 - 12:05

score 136 · Answer 13 · 2026-04-16 22:23:44

136

Views

Invertible elements of $K[x]/\langle p(x)\rangle$ when $p(x)$ is irreducible

Published on 16 Apr 2026 - 22:23

score 49 · Answer 14 · 2026-04-13 20:17:31

49

Views

For what $n$ are these polynomials separable?

Published on 13 Apr 2026 - 20:17

score 97 · Answer 15 · 2026-04-15 04:03:08

97

Views

Places of $\bar{\mathbb{Q}}$

Published on 15 Apr 2026 - 4:03

List Question

Suppose char$(F) = p$ and $E/F$ with $[E:F] = p$. Then if there is one inseparable element then every element in $E\setminus F$ is inseparable

If $G=\mathsf{Aut}_k(F)$ acts on field $F$ algebraic over $k$ then do we have: orbit $G\alpha=\text{ roots of minimal polynomial of }\alpha$?

Is there a quadratically closed field strictly between the quadratic closures of $\mathbb{Q}$ and $\mathbb{Q}(\sqrt[3]{2})$?

Number of roots of irreducible polynomials in extension fields

show that $x\in E$ is transcendental over $F$

Frobenius-endomorphism surjective $\Rightarrow$ field perfect

Let $K=\mathbb{Q}(i), L=K(\sqrt[3]{3+i}), M=K(\sqrt{\pi}/2)$. Find all $K$-automorphisms of $L$ and $M$.

Existence of irreducible Polynomials in finite fields

What is the Galois group of this extension?

Show that this extension of function fields over $\mathbb{F}_{81}$ is normal

On normal extension, a square root of discriminant is in field F?

About the primitive elements of $\mathbb{Q}(\sqrt{3},i\sqrt{5})$

Invertible elements of $K[x]/\langle p(x)\rangle$ when $p(x)$ is irreducible

For what $n$ are these polynomials separable?

Places of $\bar{\mathbb{Q}}$

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