List questions from extension-field

Published on 12 Apr 2026 - 11:30

161

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Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

Published on 25 Mar 2026 - 7:41

1k

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Degree of a field extension is a power of 2

Published on 13 Apr 2026 - 2:51

5.8k

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Elements of $\mathbb Q(2^{1/3})$

Published on 16 Apr 2026 - 17:15

181

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Prove that $K$ is not a simple extension of $\mathbb{Q}$.

Published on 15 Apr 2026 - 23:30

66

Views

Proof of $i\notin\mathbb{Q}(\alpha)$ for $\alpha$ root of irreducible polynomial with odd degree

Published on 16 Apr 2026 - 13:01

327

Views

Field extensions and inverse $ \alpha$ of an element

Published on 09 Apr 2026 - 19:11

185

Views

An isomorphism between $\mathbb F_2(\alpha )$ and $\mathbb F_2(\beta )$.

Published on 22 Apr 2026 - 15:39

30

Views

How to tell if an algebraic number is an element of another algebraic field extension?

Published on 10 Apr 2026 - 23:56

1.5k

Views

Artin-Schreier Theorem and Galois Extensions

Published on 29 Mar 2026 - 14:02

80

Views

If $F \subseteq L$ is an algebraic field extension and $\phi:L \to L$ is an $F$-monomorphism, then $\phi(L)=L$.

Published on 17 Apr 2026 - 4:05

66

Views

Elements of a Galois group: can one make this claim?

Published on 14 Apr 2026 - 5:08

385

Views

Totally transcendental extension and irreducibility.

Published on 09 Apr 2026 - 8:26

461

Views

Example of Basic Theorem of field extensions

Published on 12 Apr 2026 - 12:33

142

Views

Question about totally a transcendental extension

Published on 16 Apr 2026 - 16:20

List Question

Determining isomorphism between field extensions

Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

Degree of a field extension is a power of 2

Elements of $\mathbb Q(2^{1/3})$

Prove that $K$ is not a simple extension of $\mathbb{Q}$.

Proof of $i\notin\mathbb{Q}(\alpha)$ for $\alpha$ root of irreducible polynomial with odd degree

Field extensions and inverse $ \alpha$ of an element

An isomorphism between $\mathbb F_2(\alpha )$ and $\mathbb F_2(\beta )$.

How to tell if an algebraic number is an element of another algebraic field extension?

Artin-Schreier Theorem and Galois Extensions

If $F \subseteq L$ is an algebraic field extension and $\phi:L \to L$ is an $F$-monomorphism, then $\phi(L)=L$.

Elements of a Galois group: can one make this claim?

Totally transcendental extension and irreducibility.

Example of Basic Theorem of field extensions

Question about totally a transcendental extension

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