List questions from galois-extensions

Published on 17 Apr 2026 - 13:40

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Determine the degree of a root of $X^p-X-\alpha$ (Serge Lang Algebra exercise VI.29)

Published on 15 Apr 2026 - 7:58

93

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Elements with norm $1$ in a quadratic field

Published on 15 Apr 2026 - 9:52

139

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Action of Galois group on scheme

Published on 12 Apr 2026 - 14:12

34

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How to generate all elements of an extension field from a base field? (GF(2))

Published on 14 Apr 2026 - 23:54

37

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Splitting field of a separable (and irreducible) polynomial is separable

Published on 09 Apr 2026 - 17:13

41

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How Do I Calculate The Galois Group And Intermediate Fields Of A Certain Extension Using Magma?

Published on 11 May 2026 - 0:30

58

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Ramification of primes on $\overline{\mathbb Q}$

Published on 10 May 2026 - 14:06

152

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$b$ not a square, $a^2 − b$ a square Why is $\Bbb Q(\sqrt {a + \sqrt b})$ the splitting field of $f(x)=(t^2-a)^2-b$ and a normal extension?

Published on 14 Apr 2026 - 18:50

90

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$\Bbb Q \subseteq \Bbb Q(\sqrt {a + \sqrt b})$ is normal iff at least one of $a^2 − b$ and $(a^2 − b)/b$ is a square in $ \Bbb Q$

Published on 16 Apr 2026 - 14:31

81

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Is there an example, such that $\omega\in F(\beta)\land \omega\notin F$?

Published on 17 Apr 2026 - 3:26

43

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I ask about the galois extension proof of the fundamental theorem

Published on 12 Apr 2026 - 13:10

72

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Extending a field homomorphism on a finite field

Published on 09 Apr 2026 - 11:23

41

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Exercises about Galois theory and isomorphism type of the Galois-Group

Published on 13 Apr 2026 - 6:20

68

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Some exercises about Galois Groups and Automorphisms of a finite field extension

Published on 14 Apr 2026 - 12:50

List Question

Prove a Weaker Version of the Normal Basis Theorem

Determine the degree of a root of $X^p-X-\alpha$ (Serge Lang Algebra exercise VI.29)

Elements with norm $1$ in a quadratic field

Action of Galois group on scheme

How to generate all elements of an extension field from a base field? (GF(2))

Splitting field of a separable (and irreducible) polynomial is separable

How Do I Calculate The Galois Group And Intermediate Fields Of A Certain Extension Using Magma?

Ramification of primes on $\overline{\mathbb Q}$

$b$ not a square, $a^2 − b$ a square Why is $\Bbb Q(\sqrt {a + \sqrt b})$ the splitting field of $f(x)=(t^2-a)^2-b$ and a normal extension?

$\Bbb Q \subseteq \Bbb Q(\sqrt {a + \sqrt b})$ is normal iff at least one of $a^2 − b$ and $(a^2 − b)/b$ is a square in $ \Bbb Q$

Is there an example, such that $\omega\in F(\beta)\land \omega\notin F$?

I ask about the galois extension proof of the fundamental theorem

Extending a field homomorphism on a finite field

Exercises about Galois theory and isomorphism type of the Galois-Group

Some exercises about Galois Groups and Automorphisms of a finite field extension

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