List questions from extension-field

Published on 16 Apr 2026 - 6:41

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$\mathbb Q(\sqrt 2,\sqrt 3,\sqrt 5)=\mathbb Q(\sqrt 2+\sqrt 3+\sqrt 5)$ - Generalisation?

Published on 17 Apr 2026 - 0:19

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Minimal polynomial of a finite purely inseparable field extension

Published on 11 Apr 2026 - 11:22

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Help Determining Degree of a Field Extension

Published on 12 Apr 2026 - 7:23

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Is $x^2+1$ irreducible over a cyclotomic field?

Published on 13 Apr 2026 - 0:40

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Splitting field that isn't a Galois extension

Published on 15 Apr 2026 - 10:12

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Special elements of fields extensions

Published on 14 Apr 2026 - 22:44

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If $0\neq \alpha \in E$ is algebraic over F, then $\frac{1}{a}$ is also algebraic over F.

Published on 16 Apr 2026 - 7:20

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Field extension of $\mathbb Q$ of degree 2

Published on 15 Apr 2026 - 10:55

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Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$

Published on 17 Apr 2026 - 15:59

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If $F/L$ is normal and $L/K$ is purely inseparable, then $F/K$ is normal

Published on 16 Apr 2026 - 15:51

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exercise 19.13 in Algebra (Issac)

Published on 15 Apr 2026 - 6:09

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An element of an extension field has a rational function with coefficients in the field that equals it

Published on 14 Apr 2026 - 11:52

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Algebraically closed subfields of $\mathbb{C}$

Published on 14 Apr 2026 - 12:59

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If $K/L$ is normal and $L/F$ is purely inseparable, then $K/F$ is normal

Published on 16 Apr 2026 - 1:11

List Question

Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree?

$\mathbb Q(\sqrt 2,\sqrt 3,\sqrt 5)=\mathbb Q(\sqrt 2+\sqrt 3+\sqrt 5)$ - Generalisation?

Minimal polynomial of a finite purely inseparable field extension

Help Determining Degree of a Field Extension

Is $x^2+1$ irreducible over a cyclotomic field?

Splitting field that isn't a Galois extension

Special elements of fields extensions

If $0\neq \alpha \in E$ is algebraic over F, then $\frac{1}{a}$ is also algebraic over F.

Field extension of $\mathbb Q$ of degree 2

Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$

If $F/L$ is normal and $L/K$ is purely inseparable, then $F/K$ is normal

exercise 19.13 in Algebra (Issac)

An element of an extension field has a rational function with coefficients in the field that equals it

Algebraically closed subfields of $\mathbb{C}$

If $K/L$ is normal and $L/F$ is purely inseparable, then $K/F$ is normal

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