List questions from field-theory

Published on 26 Mar 2026 - 22:55

92

Views

$\gcd$ of polynomials over a finite field

Published on 11 Apr 2026 - 11:02

93

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Galois group of $x^4+tx+t\in F(t)[x]$

Published on 17 Apr 2026 - 12:33

72

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Is the field characteristic necessary for this diagonalization question?

Published on 25 Mar 2026 - 11:53

354

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Galois Theory without the Primitive Element Theorem

Published on 29 Mar 2026 - 2:45

89

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How do I show $[\mathbb{Q}(\alpha):\mathbb{Q}]=4$.

Published on 25 Apr 2026 - 6:40

448

Views

Any valuation ring of $\mathbb Q$ is $\mathbb Z_{(p)}$ for some prime $p$

Published on 26 Mar 2026 - 12:07

205

Views

If a polynomial is irreducible and nonconstant over a finite field, it has a multiple root iff it is in the variable $x^p$

Published on 16 Apr 2026 - 5:22

65

Views

Prove that the following algebraic system is a field for $a,b \in \mathbb Q$, but not for $a,b \in \mathbb R$.

Published on 15 Apr 2026 - 21:12

76

Views

Number of $\alpha\in\Bbb{F}_{27}$ such that $|A_{\alpha}|=26$ equals $12$

Published on 15 Apr 2026 - 18:37

45

Views

Linear maps over division rings

Published on 10 Apr 2026 - 8:22

101

Views

Proof of homomorphism theorem in S. Langs Algebra

Published on 25 Apr 2026 - 11:27

43

Views

Existence of an algebraic function on a disc, in an elementary way

Published on 12 Apr 2026 - 17:39

1.4k

Views

What are the operations in quaternions as a division ring?

Published on 11 Apr 2026 - 5:55

105

Views

Is the sum of polynomials solvable by radicals if both polynomials are solvable by radicals?

Published on 14 Apr 2026 - 1:29

List Question

What is the Meaning of $Q[u_1] \cong Q[x]/\langle f(x)\rangle$?

$\gcd$ of polynomials over a finite field

Galois group of $x^4+tx+t\in F(t)[x]$

Is the field characteristic necessary for this diagonalization question?

Galois Theory without the Primitive Element Theorem

How do I show $[\mathbb{Q}(\alpha):\mathbb{Q}]=4$.

Any valuation ring of $\mathbb Q$ is $\mathbb Z_{(p)}$ for some prime $p$

If a polynomial is irreducible and nonconstant over a finite field, it has a multiple root iff it is in the variable $x^p$

Prove that the following algebraic system is a field for $a,b \in \mathbb Q$, but not for $a,b \in \mathbb R$.

Number of $\alpha\in\Bbb{F}_{27}$ such that $|A_{\alpha}|=26$ equals $12$

Linear maps over division rings

Proof of homomorphism theorem in S. Langs Algebra

Existence of an algebraic function on a disc, in an elementary way

What are the operations in quaternions as a division ring?

Is the sum of polynomials solvable by radicals if both polynomials are solvable by radicals?

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