List questions from field-theory

Published on 10 May 2026 - 18:29

76

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Find smallest $n$ so that $Gal(K(\xi)/K)$ is not cyclic

Published on 15 Apr 2026 - 3:05

92

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Identify the property of Galois group

Published on 14 Apr 2026 - 6:19

203

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Isomorphic subgroups of the multiplicative group of a field

Published on 13 Apr 2026 - 23:28

44

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Explicit isomorphism of tensor product of fields $L \otimes_K L$

Published on 13 Apr 2026 - 10:30

114

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Let $F$ be a field with characteristic 0, and $p(x)\in F[x]$ be an irreducible polynomial of degree 3 with root $\alpha$. Show $F(\alpha)=F(\alpha^2)$

Published on 16 Apr 2026 - 14:49

106

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A proof of a special case of Dirichlet's theorem.

Published on 11 Apr 2026 - 14:37

70

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$F(a_1,\ldots,a_{n-1})(a_n)=F(a_1,\ldots,a_n)$

Published on 15 Apr 2026 - 22:19

62

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Showing that field embedding exists

Published on 15 Apr 2026 - 4:02

55

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Factoring a binary form over a algebraically closed field

Published on 13 Apr 2026 - 21:00

51

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Lang exercise 50 on Witt vectors

Published on 15 Apr 2026 - 7:56

75

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What is $[\mathbb{Q}(\zeta+\zeta^{-1},\zeta^t):\mathbb{Q}(\zeta+\zeta^{-1})]$?

Published on 17 Apr 2026 - 8:31

104

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Is it true that $\mathbb R(x,y)\otimes_{\mathbb R} \mathbb C=\mathbb C(x,y)$

Published on 14 Apr 2026 - 3:56

480

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Some easy examples of operations that don't work like you'd expect them to, i.e. not being commutative or associative etc.

Published on 16 Apr 2026 - 20:06

38

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Question about the degree of the splitting field of $X^4-2X^2-2$

Published on 14 Apr 2026 - 12:21

List Question

What's a direct or quickest proof of simple zeros lift to factorizations lift?

Find smallest $n$ so that $Gal(K(\xi)/K)$ is not cyclic

Identify the property of Galois group

Isomorphic subgroups of the multiplicative group of a field

Explicit isomorphism of tensor product of fields $L \otimes_K L$

Let $F$ be a field with characteristic 0, and $p(x)\in F[x]$ be an irreducible polynomial of degree 3 with root $\alpha$. Show $F(\alpha)=F(\alpha^2)$

A proof of a special case of Dirichlet's theorem.

$F(a_1,\ldots,a_{n-1})(a_n)=F(a_1,\ldots,a_n)$

Showing that field embedding exists

Factoring a binary form over a algebraically closed field

Lang exercise 50 on Witt vectors

What is $[\mathbb{Q}(\zeta+\zeta^{-1},\zeta^t):\mathbb{Q}(\zeta+\zeta^{-1})]$?

Is it true that $\mathbb R(x,y)\otimes_{\mathbb R} \mathbb C=\mathbb C(x,y)$

Some easy examples of operations that don't work like you'd expect them to, i.e. not being commutative or associative etc.

Question about the degree of the splitting field of $X^4-2X^2-2$

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