List questions from extension-field

Published on 26 Mar 2026 - 17:32

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is galois group always finite?

Published on 12 Apr 2026 - 2:55

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Does $L_1(w)=L_2(w)$ imply $L_1=L_2$?

Published on 11 Apr 2026 - 17:04

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Definition of separable extension via $k$-algebra homomorphisms

Published on 14 Apr 2026 - 19:41

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$Gal(F/k) \cong \langle k^{^{n}}, a_1, \ldots, a_n \rangle / \langle k^{^{n}} \rangle$

Published on 15 Apr 2026 - 18:13

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For non-algebraically closed field $k$ and integer $n>1$, there is a polynomial in $n$-variables over $k$ having only one zero in $k^n$

Published on 23 Feb 2026 - 16:27

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Are the class numbers for the field $\Bbb{Q}(e^{\pi i/n})$ $1$ for all prime $n$?

Published on 26 Mar 2026 - 3:12

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Let $p$ be a prime and let $F$ be a field with $p^k$ elements and $K$ a subfield. Show that $Gal(F : K)$ is a cyclic group of order $[F : K]$.

Published on 16 Apr 2026 - 4:58

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A question about field of fractions of a ring of functions

Published on 12 Apr 2026 - 13:11

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Proving $M: \mathbb Q$ may not be a Galois Extension

Published on 26 Mar 2026 - 4:52

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How many subfields of $\mathbb Q(\zeta_{16})$ for which $[L:\mathbb Q]=2$?

Published on 26 Mar 2026 - 3:11

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Galois Descent of morphisms for field extensions

Published on 11 Apr 2026 - 11:16

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$(K(a))^p = K^p(a^p) $

Published on 16 Apr 2026 - 17:57

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Example of an extension where Normal of a Normal extension is Normal.

Published on 16 Apr 2026 - 0:17

219

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Has $x^3 - x +1$ a root in $\mathbb{Q}(a)$?

Published on 16 Apr 2026 - 14:53

List Question

Proving that $\sum_{v\in M_K, \,\,v\text{ archim.}} n_v=[K:\mathbb{Q}]$

is galois group always finite?

Does $L_1(w)=L_2(w)$ imply $L_1=L_2$?

Definition of separable extension via $k$-algebra homomorphisms

$Gal(F/k) \cong \langle k^{^{n}}, a_1, \ldots, a_n \rangle / \langle k^{^{n}} \rangle$

For non-algebraically closed field $k$ and integer $n>1$, there is a polynomial in $n$-variables over $k$ having only one zero in $k^n$

Are the class numbers for the field $\Bbb{Q}(e^{\pi i/n})$ $1$ for all prime $n$?

Let $p$ be a prime and let $F$ be a field with $p^k$ elements and $K$ a subfield. Show that $Gal(F : K)$ is a cyclic group of order $[F : K]$.

A question about field of fractions of a ring of functions

Proving $M: \mathbb Q$ may not be a Galois Extension

How many subfields of $\mathbb Q(\zeta_{16})$ for which $[L:\mathbb Q]=2$?

Galois Descent of morphisms for field extensions

$(K(a))^p = K^p(a^p) $

Example of an extension where Normal of a Normal extension is Normal.

Has $x^3 - x +1$ a root in $\mathbb{Q}(a)$?

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