List questions from field-theory

Published on 10 Apr 2026 - 12:59

608

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Existence of finite field extension containing a root

Published on 11 Apr 2026 - 7:22

32

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If $k$ is a field then $\text{End}_k(k^2)$ is simple

Published on 04 Sep 2014 - 15:47

61

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A field $K$ is an algebra

Published on 12 Apr 2026 - 4:29

98

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Algebraic extension of rational numbers.

Published on 10 Apr 2026 - 3:38

276

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Proof of a Field Extensions Theorem

Published on 11 Apr 2026 - 15:15

186

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Give an example of a field where -1=1

Published on 06 Sep 2014 - 21:31

124

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Can the product of only some of the algebraic conjugates be an integer?

Published on 28 Mar 2026 - 6:16

52

Views

On the Characterization of $F[\alpha]$ for a Field Extension $E/F$.

Published on 07 Sep 2014 - 19:44

566

Views

Why is ring of integers $\mathcal O_K$ called ring of integers - what properties of $\mathbb{Z}$ does it inherit?

Published on 13 Apr 2026 - 4:37

101

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$[F(t):F(t^n)]=n$ where $t$ is trascendental

Published on 04 Apr 2026 - 7:26

470

Views

When $\mathbb{Q}(\alpha+\beta)=\mathbb{Q}(\alpha, \beta)$?

Published on 02 Apr 2026 - 8:46

109

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$F(x,y)$ over $F$ is not simple

Published on 12 Apr 2026 - 18:49

4.6k

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clarification of algebraic closure and algebraically closed field

Published on 02 Apr 2026 - 10:45

83

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$\alpha \in \Omega_{\mathbb Q}^{x^3-2}$(splitting field) is such that $\alpha^5 \in \mathbb Q$ then $\alpha \in \mathbb Q$

Published on 26 Mar 2026 - 6:30

List Question

Calculating Splitting field

Existence of finite field extension containing a root

If $k$ is a field then $\text{End}_k(k^2)$ is simple

A field $K$ is an algebra

Algebraic extension of rational numbers.

Proof of a Field Extensions Theorem

Give an example of a field where -1=1

Can the product of only some of the algebraic conjugates be an integer?

On the Characterization of $F[\alpha]$ for a Field Extension $E/F$.

Why is ring of integers $\mathcal O_K$ called ring of integers - what properties of $\mathbb{Z}$ does it inherit?

$[F(t):F(t^n)]=n$ where $t$ is trascendental

When $\mathbb{Q}(\alpha+\beta)=\mathbb{Q}(\alpha, \beta)$?

$F(x,y)$ over $F$ is not simple

clarification of algebraic closure and algebraically closed field

$\alpha \in \Omega_{\mathbb Q}^{x^3-2}$(splitting field) is such that $\alpha^5 \in \mathbb Q$ then $\alpha \in \mathbb Q$

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