List questions from field-theory

Published on 12 Apr 2026 - 15:00

137

Views

Issue in theorem 9.1 Serge Lang algebra

Published on 13 Apr 2026 - 23:29

51

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$x^{\frac{p-1}{2}}+1$ is reducible in $\Bbb Z_p[x]$

Published on 16 Apr 2026 - 12:38

97

Views

If $\mathbb Q[a,b]$ is a field, then are $a$ and $b$ algebraic?

Published on 17 Apr 2026 - 9:22

45

Views

minimal polynomial over $\mathbb{Z}_7(t^{14})$

Published on 13 Apr 2026 - 11:17

90

Views

Help with understanding radical extensions in Galois theory (decomposition field of the polynomial $X^n-a$ over $k$)

Published on 11 Apr 2026 - 4:46

47

Views

The map $\phi:Gal(KL/L)\to Gal(K/F)$ is well defined

Published on 14 Apr 2026 - 23:34

91

Views

Field automorphisms of $F(x)$

Published on 14 Apr 2026 - 8:54

42

Views

Algebraic independence of solutions

Published on 12 Apr 2026 - 13:16

55

Views

Number of ways to represent an integer $n$ in a finite field $\mathbb F_{p^m}$ as a sum of two squares

Published on 16 Apr 2026 - 3:16

71

Views

Factorization over $\mathbb{Q}$ and $\mathbb{Z_{41}}$

Published on 14 Apr 2026 - 2:22

120

Views

There are infinitely many prime number $p$ such that $p≡3\pmod4$ and $p$ splits completely in $K$.

Published on 16 Apr 2026 - 6:11

53

Views

Is there an extension of a function field of degree $n$ for every $n$?

Published on 12 Apr 2026 - 10:49

49

Views

Is it possible for an incompletely valued field to have a finite-degree extension which is complete?

Published on 09 Apr 2026 - 15:04

140

Views

How is the field extension finite

Published on 13 Apr 2026 - 23:45

List Question

Pairs with relations

Issue in theorem 9.1 Serge Lang algebra

$x^{\frac{p-1}{2}}+1$ is reducible in $\Bbb Z_p[x]$

If $\mathbb Q[a,b]$ is a field, then are $a$ and $b$ algebraic?

minimal polynomial over $\mathbb{Z}_7(t^{14})$

Help with understanding radical extensions in Galois theory (decomposition field of the polynomial $X^n-a$ over $k$)

The map $\phi:Gal(KL/L)\to Gal(K/F)$ is well defined

Field automorphisms of $F(x)$

Algebraic independence of solutions

Number of ways to represent an integer $n$ in a finite field $\mathbb F_{p^m}$ as a sum of two squares

Factorization over $\mathbb{Q}$ and $\mathbb{Z_{41}}$

There are infinitely many prime number $p$ such that $p≡3\pmod4$ and $p$ splits completely in $K$.

Is there an extension of a function field of degree $n$ for every $n$?

Is it possible for an incompletely valued field to have a finite-degree extension which is complete?

How is the field extension finite

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