List questions from extension-field

Published on 12 Apr 2026 - 20:22

976

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Is a prime ideal in the polynomial ring over an algebraically closed field prime also in polynomial rings over extension fields?

Published on 13 Apr 2026 - 5:10

119

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Comparing fields with same degree

Published on 09 Apr 2026 - 19:45

2.1k

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Do maximal proper subfields of the real numbers exist?

Published on 10 Apr 2026 - 3:11

425

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This tower of fields is being ridiculous

Published on 13 Apr 2026 - 19:07

8.5k

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Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

Published on 16 Apr 2026 - 6:02

128

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Primitive element (fields)

Published on 13 Apr 2026 - 16:44

323

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On the fundamental theorem of field extensions

Published on 12 Apr 2026 - 10:16

1.5k

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Radical extensions

Published on 11 Apr 2026 - 22:32

294

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Proof that field extensions of degree 3 over $K$ with $\mathrm{char}(K) \neq 3$ are separable

Published on 13 Apr 2026 - 21:00

70

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$a\in \mathbb{C}$ for which $[ \mathbb{Q}(a) : \mathbb{Q}(a^3) ] = 2$.

Published on 16 Apr 2026 - 15:50

690

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$\mathbb Q$-basis of $\mathbb Q(\sqrt[3] 7, \sqrt[5] 3)$.

Published on 17 Apr 2026 - 10:06

1.4k

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Why $\mathbb Q(i, \sqrt{-2}) : \mathbb Q$ is an extension of degree 4

Published on 15 Apr 2026 - 23:51

29

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How to prove $[\mathbb Q(\zeta_{p^k}): \mathbb Q] = (p-1)*p^{k-1}$?

Published on 16 Apr 2026 - 11:38

240

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When a subfield of a splitting field is a splitting field

Published on 11 Apr 2026 - 21:35

List Question

Generalized Rationalization in Finite Radical Field Extensions

Is a prime ideal in the polynomial ring over an algebraically closed field prime also in polynomial rings over extension fields?

Comparing fields with same degree

Do maximal proper subfields of the real numbers exist?

This tower of fields is being ridiculous

Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

Primitive element (fields)

On the fundamental theorem of field extensions

Radical extensions

Proof that field extensions of degree 3 over $K$ with $\mathrm{char}(K) \neq 3$ are separable

$a\in \mathbb{C}$ for which $[ \mathbb{Q}(a) : \mathbb{Q}(a^3) ] = 2$.

$\mathbb Q$-basis of $\mathbb Q(\sqrt[3] 7, \sqrt[5] 3)$.

Why $\mathbb Q(i, \sqrt{-2}) : \mathbb Q$ is an extension of degree 4

How to prove $[\mathbb Q(\zeta_{p^k}): \mathbb Q] = (p-1)*p^{k-1}$?

When a subfield of a splitting field is a splitting field

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