List questions from field-theory

Published on 10 Apr 2026 - 22:46

295

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Proposition about of Purely inseparable extension

Published on 09 Apr 2026 - 6:02

209

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Computing a Galois group

Published on 12 Apr 2026 - 20:23

94

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Irreducible Polynomial in $\mathbb{Q}[x]$

Published on 17 Apr 2026 - 7:24

792

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All automorphisms of splitting fields

Published on 16 Apr 2026 - 15:54

202

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$V$ is finite dimentional over field $K\iff$ field extension $L/K$ is finite

Published on 12 Apr 2026 - 4:04

145

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Etymology of normal extensions and subgroups

Published on 13 Apr 2026 - 20:53

174

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How to show the isomorphism

Published on 09 Apr 2026 - 1:39

1.3k

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Let R be a ring with unity $1_R$ and let S (with unity $1_S$) be a subring of R. Prove that either $1_S=1_R$ or $1_S$ is a zero divisor of R.

Published on 16 Apr 2026 - 8:56

807

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If $f$ is irreducible over a perfect field, then $f$ has no multiple zeros.

Published on 14 Apr 2026 - 0:03

659

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Computing the galois group of $x^3+3x+1$

Published on 15 Apr 2026 - 1:36

38

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$F\subset L \subset F[a]$ fields, prove L is created by $f_a$

Published on 14 Apr 2026 - 16:56

342

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Generated field is the same as composite field

Published on 13 Apr 2026 - 4:26

386

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Galois group of the polynomial $x^4-4x^2-11$ over $\mathbb{Q}$

Published on 16 Apr 2026 - 1:35

335

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Theorem about equivalent norms.

Published on 12 Apr 2026 - 6:32

List Question

Question about polynomials in finite fields

Proposition about of Purely inseparable extension

Computing a Galois group

Irreducible Polynomial in $\mathbb{Q}[x]$

All automorphisms of splitting fields

$V$ is finite dimentional over field $K\iff$ field extension $L/K$ is finite

Etymology of normal extensions and subgroups

How to show the isomorphism

Let R be a ring with unity $1_R$ and let S (with unity $1_S$) be a subring of R. Prove that either $1_S=1_R$ or $1_S$ is a zero divisor of R.

If $f$ is irreducible over a perfect field, then $f$ has no multiple zeros.

Computing the galois group of $x^3+3x+1$

$F\subset L \subset F[a]$ fields, prove L is created by $f_a$

Generated field is the same as composite field

Galois group of the polynomial $x^4-4x^2-11$ over $\mathbb{Q}$

Theorem about equivalent norms.

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