List questions from field-theory

Published on 24 Apr 2026 - 23:50

61

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Why is the generalized definition of valued field automatically non-Archimedean?

Published on 09 Apr 2026 - 4:13

39

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Need a proof for a lemma (Stewart. Galois Theory. Lemma 5.14, about the dimension of simple extensions)

Published on 15 Apr 2026 - 9:58

56

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Are the exponential and matrix exponential valid over an arbitrary field $\mathbb{F}$?

Published on 16 Apr 2026 - 0:30

87

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Does $2y^2=4+17x^4$ have solutions in $\Bbb{Q}_2(\sqrt{-3})$?

Published on 15 May 2026 - 17:51

15

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What is $\text{trdeg}(F( X_i Y_j \mid 1 \leq i \leq n, 1 \leq j \leq m) / F)$?

Published on 18 Apr 2026 - 15:47

72

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does the residue field of an algebraically closed valued field lift?

Published on 14 Apr 2026 - 2:08

132

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Does the SVD work on an incomplete field?

Published on 13 Apr 2026 - 15:41

50

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Known "families" of algebraic numbers

Published on 15 May 2026 - 11:21

27

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If $I=F$ , $K/S$ purely inseparable, $S/F$ separable then $K/I$ is not separable

Published on 09 Apr 2026 - 15:23

49

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Order of galois group of splitting field

Published on 11 Apr 2026 - 8:07

71

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Ask for help on proving irreducible polynomial on $K[x]$

Published on 17 Apr 2026 - 3:31

90

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Is this map $\mathbb Q(x, y) \to \mathbb Q((t))$ well-defined?

Published on 17 Apr 2026 - 5:07

99

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Does $(3+2\sqrt{-2})y^2=1+12\sqrt{-2}-4・17x^4$ have solution in $\Bbb{Q}_{17}$?

Published on 15 Apr 2026 - 16:57

55

Views

Dimension of $\mathbb{Q(\omega)}$ and minimal polynomial of $\sqrt[3]{2}$

Published on 17 Apr 2026 - 14:32

List Question

$D$ domain, $M,N$ $D$-modules, $M$ divisible then $\hom_{D}(M,N)$ is a $D$-module has no torsion.

Why is the generalized definition of valued field automatically non-Archimedean?

Need a proof for a lemma (Stewart. Galois Theory. Lemma 5.14, about the dimension of simple extensions)

Are the exponential and matrix exponential valid over an arbitrary field $\mathbb{F}$?

Does $2y^2=4+17x^4$ have solutions in $\Bbb{Q}_2(\sqrt{-3})$?

What is $\text{trdeg}(F( X_i Y_j \mid 1 \leq i \leq n, 1 \leq j \leq m) / F)$?

does the residue field of an algebraically closed valued field lift?

Does the SVD work on an incomplete field?

Known "families" of algebraic numbers

If $I=F$ , $K/S$ purely inseparable, $S/F$ separable then $K/I$ is not separable

Order of galois group of splitting field

Ask for help on proving irreducible polynomial on $K[x]$

Is this map $\mathbb Q(x, y) \to \mathbb Q((t))$ well-defined?

Does $(3+2\sqrt{-2})y^2=1+12\sqrt{-2}-4・17x^4$ have solution in $\Bbb{Q}_{17}$?

Dimension of $\mathbb{Q(\omega)}$ and minimal polynomial of $\sqrt[3]{2}$

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