List questions from field-theory

Published on 13 Apr 2026 - 4:45

29

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$Q⊂L$ is a field extension with $ [L : Q] = 32$. Show that 2 is not a third power in $L$.

Published on 16 Apr 2026 - 0:52

101

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Is every absolute value defined on $\Bbb R$ or $\Bbb C$ not differentiable at zero?

Published on 13 Apr 2026 - 15:59

192

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Galois extenstion of rational function field $\mathbb{C}(X,Y,Z)$

Published on 16 Apr 2026 - 6:25

55

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Polynomial roots and sets

Published on 18 Apr 2026 - 22:58

135

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Polynomial divisibility and automorphisms of cyclotomic fields

Published on 15 Apr 2026 - 9:12

76

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Logarithm properties in fields in general

Published on 04 May 2026 - 18:00

58

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Why do minimal polynomial have coefficients in the integral closured ring?

Published on 15 Apr 2026 - 13:04

429

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Show that $\mathbb{Q}[\sqrt{2}]$ is a field

Published on 15 Apr 2026 - 4:15

397

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Uniqueness of homomorphism

Published on 15 Apr 2026 - 13:58

2.2k

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Prove that for any prime number (p) there exist a field with $p^2$ elements

Published on 16 Apr 2026 - 23:19

215

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Extension degree of galois closure of $\mathbb{R}(X^4 -\frac{1}{X^4 })$

Published on 15 Apr 2026 - 10:02

153

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Solving problems of the form $[\mathbb Q(\omega):\mathbb Q]$, where $\omega=\cos(\frac {2\theta\pi}\phi)+i\sin(\frac {2\theta\pi}\phi)$.

Published on 17 Apr 2026 - 11:12

177

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Primitive element extension of discrete valuation ring.

Published on 16 Apr 2026 - 9:49

394

Views

Ideals of a polynomial ring $R[x]$ - example

Published on 16 Apr 2026 - 8:19

List Question

How to do subtraction over Galois field or finite field?

$Q⊂L$ is a field extension with $ [L : Q] = 32$. Show that 2 is not a third power in $L$.

Is every absolute value defined on $\Bbb R$ or $\Bbb C$ not differentiable at zero?

Galois extenstion of rational function field $\mathbb{C}(X,Y,Z)$

Polynomial roots and sets

Polynomial divisibility and automorphisms of cyclotomic fields

Logarithm properties in fields in general

Why do minimal polynomial have coefficients in the integral closured ring?

Show that $\mathbb{Q}[\sqrt{2}]$ is a field

Uniqueness of homomorphism

Prove that for any prime number (p) there exist a field with $p^2$ elements

Extension degree of galois closure of $\mathbb{R}(X^4 -\frac{1}{X^4 })$

Solving problems of the form $[\mathbb Q(\omega):\mathbb Q]$, where $\omega=\cos(\frac {2\theta\pi}\phi)+i\sin(\frac {2\theta\pi}\phi)$.

Primitive element extension of discrete valuation ring.

Ideals of a polynomial ring $R[x]$ - example

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