List questions from field-theory

Published on 14 Apr 2026 - 0:22

64

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Transcendence degree of $F(x)$ over a field $F$

Published on 17 Apr 2026 - 5:46

54

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quick question on automorphisms of fields

Published on 10 Apr 2026 - 20:01

222

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Fifth cyclotomic polynomial over a finite field

Published on 14 Apr 2026 - 18:48

47

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Adjoin indeterminates to a field making it algebraically closed and locally compact

Published on 13 Apr 2026 - 16:44

44

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Example of non isomorphic field extensions

Published on 15 Apr 2026 - 5:57

62

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Decomposition of a polynomial of the form $X^{p^n}-X$ in finite fields.

Published on 15 Apr 2026 - 8:43

56

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Remark 2, section 4.1 in Algebra From The Viewpoint of Galois Theory

Published on 15 Apr 2026 - 5:02

26

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Normal closure of $\mathbb{Q}(\sqrt{2 + \sqrt{2}})/\mathbb{Q}$

Published on 16 Apr 2026 - 16:05

27

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Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Published on 11 Apr 2026 - 13:16

64

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Is it true that $i \in \mathbb{Q}(\sqrt{2},\xi)$, where $\xi = 1_{\frac{2\pi}{3}} = -\frac{1}{2}+i\frac{\sqrt{3}}{2}$?

Published on 15 May 2026 - 15:12

61

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Completing a proof that about field extensions

Published on 09 Apr 2026 - 10:38

34

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Continuous automorphisms of number fields

Published on 14 Apr 2026 - 8:17

28

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small side question (field theory, galois groups)

Published on 11 Apr 2026 - 15:40

49

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Aluffi Alg. Chapter 0 Exercise 7.1.3

Published on 14 Apr 2026 - 10:42

List Question

Indices in compositum and intersection of fields

Transcendence degree of $F(x)$ over a field $F$

quick question on automorphisms of fields

Fifth cyclotomic polynomial over a finite field

Adjoin indeterminates to a field making it algebraically closed and locally compact

Example of non isomorphic field extensions

Decomposition of a polynomial of the form $X^{p^n}-X$ in finite fields.

Remark 2, section 4.1 in Algebra From The Viewpoint of Galois Theory

Normal closure of $\mathbb{Q}(\sqrt{2 + \sqrt{2}})/\mathbb{Q}$

Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Is it true that $i \in \mathbb{Q}(\sqrt{2},\xi)$, where $\xi = 1_{\frac{2\pi}{3}} = -\frac{1}{2}+i\frac{\sqrt{3}}{2}$?

Completing a proof that about field extensions

Continuous automorphisms of number fields

small side question (field theory, galois groups)

Aluffi Alg. Chapter 0 Exercise 7.1.3

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