List questions from extension-field

Published on 08 Feb 2018 - 18:05

102

Views

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

Published on 09 Feb 2018 - 8:24

37

Views

Calculating minimum polynomial

Published on 10 Feb 2018 - 11:55

92

Views

About splitting fields and primitive elements.

Published on 22 Mar 2026 - 10:09

592

Views

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 11 Feb 2018 - 5:24

139

Views

Orbits of general linear groups and rational canonical form

Published on 12 Feb 2018 - 4:02

48

Views

Nonstandard Extension of the Characteristic Function

Published on 20 Mar 2026 - 3:17

58

Views

extension field of $\mathbb{Q}$

Published on 15 Feb 2018 - 7:08

590

Views

General method for finding the degree of a splitting field

Published on 15 Feb 2018 - 15:00

999

Views

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

Published on 15 Feb 2018 - 20:58

113

Views

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

Published on 25 Mar 2026 - 0:02

158

Views

How to show that $h$ is onto?

Published on 17 Feb 2018 - 18:08

855

Views

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

Published on 17 Feb 2018 - 19:01

232

Views

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 22 Mar 2026 - 12:31

444

Views

Prescribing norm and trace of elements in a finite field.

Published on 18 Feb 2018 - 17:15

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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