List questions from field-theory

Published on 11 Apr 2026 - 6:52

205

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Show a certain Galois group is abelian

Published on 11 Apr 2026 - 14:46

199

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Ring with $\frac{n+1}{2}$ squares

Published on 13 Apr 2026 - 12:28

1.4k

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Field Theory: Degree of Composite equals degree of tower field extenstions (relatively prime)?

Published on 14 Apr 2026 - 3:49

256

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Prove that a field extension is not simple

Published on 14 Apr 2026 - 4:39

884

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Degree of the extension $\Bbb Q(\sqrt{2}, \sqrt{3})/\Bbb Q(\sqrt{2})$ is at most 2

Published on 15 Apr 2026 - 18:20

339

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How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

Published on 11 Apr 2026 - 8:03

56

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Is it possible to get the same extension field E/F of F by using different homomorphisms?

Published on 11 Apr 2026 - 15:32

199

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Show that an integral domain with elements integral over $\mathbb{Q}$ is a field.

Published on 14 Apr 2026 - 21:23

156

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$F(\alpha,\beta)$ coincides with $F[\alpha,\beta]$.

Published on 15 Apr 2026 - 23:16

103

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$M/F$ is not simple

Published on 11 Apr 2026 - 23:32

460

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Solve $x \times x = 1$ in a field?

Published on 17 Apr 2026 - 12:32

32

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Splitting field of a $q$, which divides $p$, is a subset of the splitting field of $p$

Published on 14 Apr 2026 - 10:36

51

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Reference for automorphisms of field extensions with non-zero transcendence degree

Published on 12 Apr 2026 - 11:58

95

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One zero in extension field $F$ implies other zero in $F$

Published on 16 Apr 2026 - 2:20

List Question

norm of primitive generator is still primitive

Show a certain Galois group is abelian

Ring with $\frac{n+1}{2}$ squares

Field Theory: Degree of Composite equals degree of tower field extenstions (relatively prime)?

Prove that a field extension is not simple

Degree of the extension $\Bbb Q(\sqrt{2}, \sqrt{3})/\Bbb Q(\sqrt{2})$ is at most 2

How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

Is it possible to get the same extension field E/F of F by using different homomorphisms?

Show that an integral domain with elements integral over $\mathbb{Q}$ is a field.

$F(\alpha,\beta)$ coincides with $F[\alpha,\beta]$.

$M/F$ is not simple

Solve $x \times x = 1$ in a field?

Splitting field of a $q$, which divides $p$, is a subset of the splitting field of $p$

Reference for automorphisms of field extensions with non-zero transcendence degree

One zero in extension field $F$ implies other zero in $F$

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