List questions from extension-field

Published on 18 Mar 2026 - 6:49

72

Views

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

Published on 17 Mar 2026 - 7:15

75

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

Published on 15 Mar 2026 - 3:32

95

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A field extension of degree $\leq 2$

Published on 21 Mar 2026 - 13:11

40

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Field not separable

Published on 19 Mar 2026 - 3:43

73

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

Published on 17 Mar 2026 - 13:27

84

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Fields generated by elements

Published on 19 Mar 2026 - 3:46

407

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

Published on 20 Mar 2026 - 2:57

278

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Eigenvalues of an element in a field extension

Published on 19 Mar 2026 - 15:32

329

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When a product of two primitive elements is also primitive?

Published on 21 Mar 2026 - 8:35

698

Views

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

Published on 24 Mar 2026 - 11:43

1.6k

Views

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

Published on 22 Mar 2026 - 3:39

85

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Is linear disjunction a polynomial condition?

Published on 21 Mar 2026 - 18:38

196

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$f\in K[X]$ 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 20 Mar 2026 - 9:45

214

Views

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

Published on 20 Mar 2026 - 2:58

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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