List questions from extension-field

Published on 10 Apr 2026 - 12:02

105

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Degree of extension $[K(\alpha):F(\alpha)]$

Published on 15 Apr 2026 - 18:20

41

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Calculating minimum polynomial

Published on 14 Apr 2026 - 11:05

96

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About splitting fields and primitive elements.

Published on 10 May 2026 - 12:50

596

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Let $ f(x) ∈ F[x] \ $ and $ \ a ∈ F \ $. Show that $ \ f(x) \ $ and $ \ f(x + a) \ $ have the same splitting field over $ \ F $

Published on 10 May 2026 - 12:55

142

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Orbits of general linear groups and rational canonical form

Published on 14 Apr 2026 - 2:08

56

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Nonstandard Extension of the Characteristic Function

Published on 29 Apr 2026 - 12:24

62

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extension field of $\mathbb{Q}$

Published on 16 Apr 2026 - 10:34

593

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General method for finding the degree of a splitting field

Published on 09 Apr 2026 - 4:51

1k

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Galois group of $(x^5-3)(x^5-7)$ over $\Bbb Q$

Published on 16 Apr 2026 - 14:46

115

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Which field has the property that there is an irreducible polynomial of any degree over it?

Published on 15 Apr 2026 - 13:16

162

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How to show that $h$ is onto?

Published on 11 Apr 2026 - 7:07

858

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What does it mean for an element to generate a field as an F-algebra?

Published on 11 Apr 2026 - 15:07

242

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For a non-zero principal ideal $I=(x)$ of a ring of integers of an algebraic number field, $|A/I|=| N_{L|\mathbb Q } (x)|$

Published on 04 May 2026 - 13:27

447

Views

Prescribing norm and trace of elements in a finite field.

Published on 15 Apr 2026 - 0:37

List Question

Properties of intermediate fields in an extension

Degree of extension $[K(\alpha):F(\alpha)]$

Calculating minimum polynomial

About splitting fields and primitive elements.

Let $ f(x) ∈ F[x] \ $ and $ \ a ∈ F \ $. Show that $ \ f(x) \ $ and $ \ f(x + a) \ $ have the same splitting field over $ \ F $

Orbits of general linear groups and rational canonical form

Nonstandard Extension of the Characteristic Function

extension field of $\mathbb{Q}$

General method for finding the degree of a splitting field

Galois group of $(x^5-3)(x^5-7)$ over $\Bbb Q$

Which field has the property that there is an irreducible polynomial of any degree over it?

How to show that $h$ is onto?

What does it mean for an element to generate a field as an F-algebra?

For a non-zero principal ideal $I=(x)$ of a ring of integers of an algebraic number field, $|A/I|=| N_{L|\mathbb Q } (x)|$

Prescribing norm and trace of elements in a finite field.

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