List questions from field-theory

Published on 12 Apr 2026 - 0:35

89

Views

For every function field $F/K$ there exists $x\in F$ with $F/K(x)$ separable

Published on 25 Mar 2026 - 1:31

59

Views

The elements of $\frac{\mathbb{Z_n}[x]}{\langle ax+b \rangle}$

Published on 14 Apr 2026 - 15:14

155

Views

A maximal ideal $M$ of $R[x]$ contains an element that is not a zero divisor

Published on 16 Apr 2026 - 15:50

56

Views

two extension fields with coprime degrees

Published on 13 Apr 2026 - 3:13

333

Views

ring homomorphism form $\mathbb{Z[x,y]} $ to $\frac{\mathbb{F_2[x]}}{\langle x^3+x^2+x+1 \rangle}$

Published on 17 Apr 2026 - 10:26

1.1k

Views

Composite of Galois extensions is Galois, a particular proof.

Published on 13 Apr 2026 - 16:12

34

Views

Algebraic independence of the roots of a biquadratic equation

Published on 25 Mar 2026 - 15:53

270

Views

Question about a degree 6 Galois extension $K(\omega) : \mathbb{Q}$

Published on 13 Apr 2026 - 0:39

69

Views

Proving the minimal polynomial of a ground field is reducible in an extension

Published on 03 Apr 2026 - 14:51

113

Views

Multiplication of degrees of field extensions over $\mathbb{Q}$

Published on 19 Nov 2019 - 1:32

652

Views

Any finite extension of Q is simple extension?

Published on 16 Apr 2026 - 14:26

136

Views

Finding all the intermediate subfields

Published on 28 Mar 2026 - 7:53

413

Views

Examples of real places of a field K

Published on 14 Apr 2026 - 14:27

95

Views

$L\otimes_K L$ reduced and $\text{ker}(L\otimes_K L\to L)$

Published on 15 Apr 2026 - 8:44

List Question

Does multiplying two intermediate fields give a subfield?

For every function field $F/K$ there exists $x\in F$ with $F/K(x)$ separable

The elements of $\frac{\mathbb{Z_n}[x]}{\langle ax+b \rangle}$

A maximal ideal $M$ of $R[x]$ contains an element that is not a zero divisor

two extension fields with coprime degrees

ring homomorphism form $\mathbb{Z[x,y]} $ to $\frac{\mathbb{F_2[x]}}{\langle x^3+x^2+x+1 \rangle}$

Composite of Galois extensions is Galois, a particular proof.

Algebraic independence of the roots of a biquadratic equation

Question about a degree 6 Galois extension $K(\omega) : \mathbb{Q}$

Proving the minimal polynomial of a ground field is reducible in an extension

Multiplication of degrees of field extensions over $\mathbb{Q}$

Any finite extension of Q is simple extension?

Finding all the intermediate subfields

Examples of real places of a field K

$L\otimes_K L$ reduced and $\text{ker}(L\otimes_K L\to L)$

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