List questions from extension-field

Published on 15 Apr 2026 - 6:19

246

Views

Irreducibility over $\mathbb{Q}[\sqrt[n]{p}]$

Published on 15 Apr 2026 - 9:33

93

Views

Doubt in Lang's proof of solvable extensions forming a distinguished class of extensions

Published on 11 Apr 2026 - 19:09

29

Views

Proving the Existence of an Intermediate Field with Special Properties in an Inseparable Field Extension

Published on 15 Apr 2026 - 0:06

60

Views

Composition of two simple field extension with coprime degree is simple?

Published on 14 Apr 2026 - 23:24

98

Views

Is every polynomial of even degree reducible after some field extensions of degree 2?

Published on 15 Apr 2026 - 9:33

63

Views

Invertible Elements of a field

Published on 16 Apr 2026 - 15:08

452

Views

Minimal polynomial of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}$

Published on 16 Apr 2026 - 1:50

47

Views

Understanding the proof of uniqueness of splitting fields.

Published on 08 Apr 2026 - 22:09

109

Views

Question about Weil Pairing & the MOV attack

Published on 15 Apr 2026 - 6:51

110

Views

Order of the Galois Group is $|G(E/F)| = [E:F_G]$ where $F_G$ is the field fixed by $G$

Published on 16 Apr 2026 - 16:07

31

Views

Differential algebraicity and transcendence degree

Published on 14 Apr 2026 - 21:05

68

Views

Why totally positive elements of a number field have a root

Published on 14 Apr 2026 - 5:54

87

Views

Find the degree of the extension $\mathbb{Q}(\sqrt{11},\sqrt[3]{11}):\mathbb{Q}(\sqrt{11})$

Published on 16 Apr 2026 - 22:54

103

Views

$a$ has no $p-$th root in $K$, then show that $X^{p^n}-a$ is irreducible in $K[x]$

Published on 16 Apr 2026 - 1:09

List Question

Finding irreducible polynomial over the rationals

Irreducibility over $\mathbb{Q}[\sqrt[n]{p}]$

Doubt in Lang's proof of solvable extensions forming a distinguished class of extensions

Proving the Existence of an Intermediate Field with Special Properties in an Inseparable Field Extension

Composition of two simple field extension with coprime degree is simple?

Is every polynomial of even degree reducible after some field extensions of degree 2?

Invertible Elements of a field

Minimal polynomial of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}$

Understanding the proof of uniqueness of splitting fields.

Question about Weil Pairing & the MOV attack

Order of the Galois Group is $|G(E/F)| = [E:F_G]$ where $F_G$ is the field fixed by $G$

Differential algebraicity and transcendence degree

Why totally positive elements of a number field have a root

Find the degree of the extension $\mathbb{Q}(\sqrt{11},\sqrt[3]{11}):\mathbb{Q}(\sqrt{11})$

$a$ has no $p-$th root in $K$, then show that $X^{p^n}-a$ is irreducible in $K[x]$

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