List questions from extension-field

Published on 13 Apr 2026 - 8:38

43

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In $K(\alpha)/K$, example of different $K$-automorphisms with the same image of $\alpha$

Published on 12 Apr 2026 - 20:57

294

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The trace form is the unique non-deg. symmetric bilinear form such that ...

Published on 14 Apr 2026 - 21:56

76

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Seeing if a polynomial is irreducible over a field extension of $\Bbb Q$.

Published on 14 Apr 2026 - 5:18

75

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Show that it is impossible to find $a,b \in \mathbb{Q}$ such that $ \frac{\sqrt{5}}{10}=a+b \frac{\sqrt{3}}{7} $

Published on 17 Apr 2026 - 0:42

31

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Fields over sums of fractions and isomorphism

Published on 12 Apr 2026 - 2:55

30

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Show that the elements of $\mathbb{K}(T)$ that are algebraic over $\mathbb{K}$ are the elements of $\mathbb{K}$.

Published on 16 Apr 2026 - 6:44

52

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Find a basis for $\mathbb{Q}(\sqrt{1+\sqrt{3}})$ over $\mathbb{Q}$.

Published on 17 Apr 2026 - 5:32

154

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Cardinality of transcendental basis over field generated by algebraic independent set

Published on 12 Apr 2026 - 21:28

54

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Prove that this set is a field

Published on 14 Apr 2026 - 23:36

107

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Testing membership of elliptic curve points in subgroups of binary extension fields

Published on 14 Apr 2026 - 22:54

39

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Degree of the maximal $p$-extension inside the ring class field of conductor $p^{\alpha+1}$

Published on 13 Apr 2026 - 20:33

100

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Checking irreducibility by considering field extension

Published on 14 Apr 2026 - 5:14

65

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Generators of a field extension determine an automorphism

Published on 12 Apr 2026 - 5:00

94

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Galois group of $x^3-2$ over $\mathbb{Q}(\omega)$

Published on 12 Apr 2026 - 12:53

List Question

How do we know that β is algebraic over F?

In $K(\alpha)/K$, example of different $K$-automorphisms with the same image of $\alpha$

The trace form is the unique non-deg. symmetric bilinear form such that ...

Seeing if a polynomial is irreducible over a field extension of $\Bbb Q$.

Show that it is impossible to find $a,b \in \mathbb{Q}$ such that $ \frac{\sqrt{5}}{10}=a+b \frac{\sqrt{3}}{7} $

Fields over sums of fractions and isomorphism

Show that the elements of $\mathbb{K}(T)$ that are algebraic over $\mathbb{K}$ are the elements of $\mathbb{K}$.

Find a basis for $\mathbb{Q}(\sqrt{1+\sqrt{3}})$ over $\mathbb{Q}$.

Cardinality of transcendental basis over field generated by algebraic independent set

Prove that this set is a field

Testing membership of elliptic curve points in subgroups of binary extension fields

Degree of the maximal $p$-extension inside the ring class field of conductor $p^{\alpha+1}$

Checking irreducibility by considering field extension

Generators of a field extension determine an automorphism

Galois group of $x^3-2$ over $\mathbb{Q}(\omega)$

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