List questions from extension-field

47

Views

Let $E/F$ be algebraic extension, $f(x)\in E[x]$, then $\exists g(x)\in E[x]$ s.t. $f(x)g(x)\in F[x]$

Published on 02 Mar 2017 - 14:02

68

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a two-transitive kind of condition for Galois group for normal extensions

Published on 02 Mar 2017 - 19:20

113

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Ring of integers of $\mathbb{Q}(a)$

Published on 03 Mar 2017 - 11:05

111

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Calculating discriminant of elements of $\mathbb{Q}(a)$

Published on 25 Mar 2026 - 6:20

315

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Fields and Galois theory.

Published on 04 Mar 2017 - 19:45

243

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Prime Field Extensions Equal or Intersection Base Field

Published on 04 Apr 2026 - 12:40

301

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How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$

Published on 29 Mar 2026 - 6:30

846

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Example of a finite field extension

Published on 06 Apr 2026 - 2:39

1.3k

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Irreducible polynomial in field extension

Published on 03 Apr 2026 - 0:28

339

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Showing that a certain field extension is Galois

Published on 07 Mar 2017 - 2:45

214

Views

Algebraically dependent vs. one element can be expressed as a polynomial of the others

Published on 25 Mar 2026 - 22:10

1.4k

Views

Field Theory: Degree of Composite equals degree of tower field extenstions (relatively prime)?

Published on 09 Mar 2017 - 22:26

253

Views

Prove that a field extension is not simple

Published on 10 Mar 2017 - 9:12

881

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Degree of the extension $\Bbb Q(\sqrt{2}, \sqrt{3})/\Bbb Q(\sqrt{2})$ is at most 2

Published on 10 Mar 2017 - 17:16

337

Views

How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

Published on 26 Mar 2026 - 6:14

List Question

Let $E/F$ be algebraic extension, $f(x)\in E[x]$, then $\exists g(x)\in E[x]$ s.t. $f(x)g(x)\in F[x]$

a two-transitive kind of condition for Galois group for normal extensions

Ring of integers of $\mathbb{Q}(a)$

Calculating discriminant of elements of $\mathbb{Q}(a)$

Fields and Galois theory.

Prime Field Extensions Equal or Intersection Base Field

How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$

Example of a finite field extension

Irreducible polynomial in field extension

Showing that a certain field extension is Galois

Algebraically dependent vs. one element can be expressed as a polynomial of the others

Field Theory: Degree of Composite equals degree of tower field extenstions (relatively prime)?

Prove that a field extension is not simple

Degree of the extension $\Bbb Q(\sqrt{2}, \sqrt{3})/\Bbb Q(\sqrt{2})$ is at most 2

How to formally prove that every $F$-algebra homomorphism $E\rightarrow E $ is a linear transformation?

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