List questions from extension-field

Published on 14 Apr 2026 - 4:50

245

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How to determine the Galois Group of a polynomial with "ugly" roots?

Published on 12 Apr 2026 - 12:13

66

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separable polynomial definition 2

Published on 12 Apr 2026 - 10:52

1.6k

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Compositum of separable extension

Published on 11 Apr 2026 - 10:11

534

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When are simple field extension for conjugate elements not only isomorphic but the same?

Published on 12 Apr 2026 - 21:40

95

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Find a concrete example of non-principality of the codifferent and different ideal of a number field

Published on 14 Apr 2026 - 18:49

593

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Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?

Published on 15 Apr 2026 - 20:43

1k

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Question about degree of a irreducible polynomial and field extensions

Published on 11 Apr 2026 - 22:29

115

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Is $F(u) =F(u^2)$?

Published on 12 Apr 2026 - 1:54

146

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Question about algebraic extension of fields

Published on 11 Apr 2026 - 13:14

609

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Find the degree of extension $\Bbb Q(ζ_9 + ζ^{−1}_ 9 )$ over $\Bbb Q$

Published on 16 Apr 2026 - 0:34

152

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Question of finding the degree of extension $ \Bbb Q( \sqrt[3]2,ζ_3\sqrt[ 3] {2}) $

Published on 15 Apr 2026 - 6:51

127

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Prove that $E$ is a finite extension of $F$ and $[E:F] \leq n$.

Published on 21 Apr 2026 - 21:32

144

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Finding the degree of $\Bbb Q(\zeta_9)$

Published on 12 Apr 2026 - 23:48

76

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Problems understanding proof of a theorem within field theory.

Published on 08 Apr 2026 - 13:36

List Question

Isomorphism of an extension field of a field of finite transcendence degree

How to determine the Galois Group of a polynomial with "ugly" roots?

separable polynomial definition 2

Compositum of separable extension

When are simple field extension for conjugate elements not only isomorphic but the same?

Find a concrete example of non-principality of the codifferent and different ideal of a number field

Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?

Question about degree of a irreducible polynomial and field extensions

Is $F(u) =F(u^2)$?

Question about algebraic extension of fields

Find the degree of extension $\Bbb Q(ζ_9 + ζ^{−1}_ 9 )$ over $\Bbb Q$

Question of finding the degree of extension $ \Bbb Q( \sqrt[3]2,ζ_3\sqrt[ 3] {2}) $

Prove that $E$ is a finite extension of $F$ and $[E:F] \leq n$.

Finding the degree of $\Bbb Q(\zeta_9)$

Problems understanding proof of a theorem within field theory.

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