List questions from field-theory

Published on 28 Mar 2026 - 6:23

357

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Maximal abelian extension v/s maximal cyclotomic extension

Published on 28 Mar 2026 - 10:16

152

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Proving a quotient ring is a field.

Published on 29 Mar 2026 - 20:55

42

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Whether $SO_k(\mathbb{Q})\subsetneq SO_k(\mathbb{Q(\sqrt{n})})$

Published on 25 Mar 2026 - 20:34

51

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If you can define division "trivially" to make a system into a Field.

Published on 06 Jun 2018 - 23:06

211

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Prove that if $[F[u]:F]$ is odd, then $F[u]=F[u^2]$

Published on 28 Mar 2026 - 10:24

73

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Finitely generated field is a finite field

Published on 26 Mar 2026 - 10:57

582

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Connections and applications of/between information (field) theory and information geometry

Published on 20 Mar 2026 - 3:58

143

Views

Creating a Straightedge, Compass and "New Tool" problem.

Published on 25 Mar 2026 - 5:59

156

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Resultant of Two Polynomials (D&F 14.6.31)

Published on 25 Mar 2026 - 11:13

59

Views

$\xi =e^{2*\pi/pi }$ , proof that is only two quadratic extention to $\Bbb Q $ that contained in $Q(\xi_p)$

Published on 28 Mar 2026 - 12:14

492

Views

Number of ring homomorphisms from a finite field to its extension

Published on 26 Mar 2026 - 11:01

40

Views

Splitting field: systematic way to list roots of minimal polynomial as elements of quotient field

Published on 25 Mar 2026 - 13:13

85

Views

Normal Basis for Galois extension $ \Bbb K / \Bbb F$ implies $ \Bbb K=\Bbb F(a)$

Published on 28 Mar 2026 - 10:04

934

Views

Polynomial decomposition into irreducible factors

Published on 25 Mar 2026 - 11:18

List Question

Galois group of $\mathbb{Q}(\sqrt{2}, \sqrt{11}) / \mathbb{Q}$

Maximal abelian extension v/s maximal cyclotomic extension

Proving a quotient ring is a field.

Whether $SO_k(\mathbb{Q})\subsetneq SO_k(\mathbb{Q(\sqrt{n})})$

If you can define division "trivially" to make a system into a Field.

Prove that if $[F[u]:F]$ is odd, then $F[u]=F[u^2]$

Finitely generated field is a finite field

Connections and applications of/between information (field) theory and information geometry

Creating a Straightedge, Compass and "New Tool" problem.

Resultant of Two Polynomials (D&F 14.6.31)

$\xi =e^{2*\pi/pi }$ , proof that is only two quadratic extention to $\Bbb Q $ that contained in $Q(\xi_p)$

Number of ring homomorphisms from a finite field to its extension

Splitting field: systematic way to list roots of minimal polynomial as elements of quotient field

Normal Basis for Galois extension $ \Bbb K / \Bbb F$ implies $ \Bbb K=\Bbb F(a)$

Polynomial decomposition into irreducible factors

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