List questions from galois-theory

Published on 21 Feb 2020 - 18:18

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If $u\in F$ is separable over $K$, then $u$ is separable over $E$.

Published on 21 Feb 2020 - 18:30

160

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Computing the Galois Group of $\mathbb{Q}\left(2^{\frac{1}{4}}\right)$ over $\mathbb{Q}$

Published on 28 Mar 2026 - 13:02

191

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How to understand the definition of prime subring in GTM 167?

Published on 22 Feb 2020 - 14:22

154

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Finding an example of field extensions satisfying certain properties

Published on 04 Apr 2026 - 5:16

184

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Equivalence of categories, related to Galois descent

Published on 25 Mar 2026 - 11:07

81

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construction of $\bigcup_{i}K_{i}$ for sequence of fields $K_{0}\subseteq K_{1}\subseteq\cdots$?

Published on 23 Feb 2020 - 9:26

45

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Does $x^4-x \in (\mathbb{Z}/2\mathbb{Z})[x]$ split completely?

Published on 26 Mar 2026 - 14:28

53

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Two reading problem in GTM173 on Page 19

Published on 24 Feb 2020 - 6:47

319

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Galois group and discriminant $\Delta_f^2$

Published on 24 Feb 2020 - 13:52

55

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How is $\mathbb{F}_p^*$ a subgroup of $\mathrm{Gal}(\mathbb{Q}_p)^{ab}$

Published on 25 Mar 2026 - 17:22

1k

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Quadratic extensions of $p$-adic fields

Published on 25 Mar 2026 - 17:24

104

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Can we construct the field extension not in the meaning of embedding?

Published on 25 Feb 2020 - 18:19

619

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Galois group of residue field extension

Published on 26 Feb 2020 - 17:08

312

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Ramified primes, as defined by Neukirch

Published on 26 Feb 2020 - 19:22

List Question

If $K\subseteq L,$ is $[L(S):L]\leq [K(S):K]$?

If $u\in F$ is separable over $K$, then $u$ is separable over $E$.

Computing the Galois Group of $\mathbb{Q}\left(2^{\frac{1}{4}}\right)$ over $\mathbb{Q}$

How to understand the definition of prime subring in GTM 167?

Finding an example of field extensions satisfying certain properties

Equivalence of categories, related to Galois descent

construction of $\bigcup_{i}K_{i}$ for sequence of fields $K_{0}\subseteq K_{1}\subseteq\cdots$?

Does $x^4-x \in (\mathbb{Z}/2\mathbb{Z})[x]$ split completely?

Two reading problem in GTM173 on Page 19

Galois group and discriminant $\Delta_f^2$

How is $\mathbb{F}_p^*$ a subgroup of $\mathrm{Gal}(\mathbb{Q}_p)^{ab}$

Quadratic extensions of $p$-adic fields

Can we construct the field extension not in the meaning of embedding?

Galois group of residue field extension

Ramified primes, as defined by Neukirch

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