List questions from extension-field

Published on 14 Apr 2015 - 14:19

617

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About subspaces of $\mathbb{R}$ as vector space over $\mathbb{Q}$.

Published on 04 Apr 2026 - 9:03

136

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When is $\mathbb{Q}(x)$ a finite extension of $\mathbb{Q}$?

Published on 14 Apr 2015 - 21:56

949

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When is the normality of field extensions transitive?

Published on 15 Apr 2015 - 2:29

86

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Discriminant of n algebraic numbers equals $0$ iff the algebraic numbers linearly dependent

Published on 15 Apr 2015 - 4:30

88

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A problem of field in abstract algebra

Published on 10 Apr 2026 - 15:06

136

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Showing two field extensions are equal

Published on 09 Apr 2026 - 9:25

154

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Field $K (x)$ of rational functions with coefficients from $K$, if $f\in K(x)$, then $f^2 \neq x^2-1$

Published on 16 Apr 2015 - 20:26

40

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About relation between degree of extension and normality

Published on 11 Apr 2026 - 5:20

69

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Prove that there are no separable extensions of $k$ of degree $n$

Published on 11 Apr 2026 - 12:39

94

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Question about field extension notation

Published on 10 Apr 2026 - 6:18

42

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prove $[E(a):E] \le [F(a):F]$

Published on 17 Apr 2015 - 17:34

263

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Q basis for splitting field

Published on 26 Mar 2026 - 21:07

1.8k

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How to find the degree of an extension field?

Published on 18 Apr 2015 - 10:49

520

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Let $a$ be a complex zero of $x^2+x+1$ over $\mathbb{Q}$. Prove that $\mathbb{Q}(\sqrt{a})=\mathbb{Q}(a)$.

Published on 18 Apr 2015 - 12:25

List Question

Finite field extensions - $K(\alpha)$

About subspaces of $\mathbb{R}$ as vector space over $\mathbb{Q}$.

When is $\mathbb{Q}(x)$ a finite extension of $\mathbb{Q}$?

When is the normality of field extensions transitive?

Discriminant of n algebraic numbers equals $0$ iff the algebraic numbers linearly dependent

A problem of field in abstract algebra

Showing two field extensions are equal

Field $K (x)$ of rational functions with coefficients from $K$, if $f\in K(x)$, then $f^2 \neq x^2-1$

About relation between degree of extension and normality

Prove that there are no separable extensions of $k$ of degree $n$

Question about field extension notation

prove $[E(a):E] \le [F(a):F]$

Q basis for splitting field

How to find the degree of an extension field?

Let $a$ be a complex zero of $x^2+x+1$ over $\mathbb{Q}$. Prove that $\mathbb{Q}(\sqrt{a})=\mathbb{Q}(a)$.

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