List questions from extension-field

Published on 06 May 2026 - 10:20

79

Views

$\overline{A}\simeq\overline{k}^n $ implies $A\simeq K_1\times\cdots\times K_r$

Published on 05 May 2026 - 12:01

87

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Extension of field, $\Bbb{R}(i \pi) = \Bbb{C} $

Published on 05 May 2026 - 4:05

108

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A field extension of degree $\leq 2$

Published on 05 May 2026 - 4:05

52

Views

Field not separable

Published on 05 May 2026 - 4:04

80

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Intersections of two primitive field extensions of $\mathbb{Q}$

Published on 05 May 2026 - 6:32

99

Views

Fields generated by elements

Published on 05 May 2026 - 4:04

413

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Find the degree of splitting field of a separable polynomial over finite field

Published on 05 May 2026 - 6:36

288

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Eigenvalues of an element in a field extension

Published on 05 May 2026 - 18:42

339

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When a product of two primitive elements is also primitive?

Published on 05 May 2026 - 8:58

705

Views

For Field extension, $[E :F]=1$ implies $E=F$

Published on 05 May 2026 - 9:40

1.7k

Views

If $\alpha$ separable over $F$ then $F(\alpha )/F$ is a separable extension.

Published on 29 Apr 2026 - 12:42

96

Views

Is linear disjunction a polynomial condition?

Published on 04 May 2026 - 2:13

202

Views

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Published on 29 Apr 2026 - 12:42

221

Views

Prove that $\mathbb{Q}[\sqrt[4](7), i] = \mathbb{Q}[\sqrt[4](7)+ i]$

Published on 07 May 2026 - 20:34

List Question

Field $\mathbb{Q}(\alpha)$ with $\alpha=\sqrt[3]7+2i$

$\overline{A}\simeq\overline{k}^n $ implies $A\simeq K_1\times\cdots\times K_r$

Extension of field, $\Bbb{R}(i \pi) = \Bbb{C} $

A field extension of degree $\leq 2$

Field not separable

Intersections of two primitive field extensions of $\mathbb{Q}$

Fields generated by elements

Find the degree of splitting field of a separable polynomial over finite field

Eigenvalues of an element in a field extension

When a product of two primitive elements is also primitive?

For Field extension, $[E :F]=1$ implies $E=F$

If $\alpha$ separable over $F$ then $F(\alpha )/F$ is a separable extension.

Is linear disjunction a polynomial condition?

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Prove that $\mathbb{Q}[\sqrt[4](7), i] = \mathbb{Q}[\sqrt[4](7)+ i]$

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