List questions from extension-field

Published on 14 Apr 2026 - 2:44

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If $\mathrm{char}(K)=p$ is prime, $L/K$ is separable if and only if $K(\alpha) =K(\alpha^p)$ for all $\alpha \in L$

Published on 15 Apr 2026 - 16:20

104

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Struggling with a question on quotients in elementary Galois theory

Published on 11 Apr 2026 - 23:37

197

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How would I pronounce the symbol $[E:F]$?

Published on 13 Apr 2026 - 2:08

58

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Elements in extension field

Published on 14 Apr 2026 - 0:12

3.9k

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Irreducible $f(x) \in F[x]$ of prime degree, $E/F$ finite extension, $p \mid [E:F]$.

Published on 15 Apr 2026 - 15:05

1.8k

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Finding a primitive element for a field extension

Published on 12 Apr 2026 - 16:59

372

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Field Extensions Problem - From Paolo Aluffi's Book

Published on 16 Apr 2026 - 23:27

117

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Galois relations between subfields

Published on 14 Apr 2026 - 23:32

1.6k

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$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?

Published on 14 Apr 2026 - 0:52

193

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How do extension fields implement $>, <$ comparisons?

Published on 10 Apr 2026 - 16:46

95

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I'm wondering definition of "E is a splitting over F"

Published on 15 Apr 2026 - 7:20

151

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An exponent of an element of a simple separable extension is contained in the base field.

Published on 16 Apr 2026 - 10:42

459

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$E/\mathbb F_q$ extension field. Show $[\mathbb F_q(\alpha) : \mathbb F_q]$ is smallest $n$ satisfying property.

Published on 16 Apr 2026 - 22:02

109

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A trace formula for an extension of complete valued fields

Published on 12 Apr 2026 - 11:42

List Question

What's the degree of the following field extension?

If $\mathrm{char}(K)=p$ is prime, $L/K$ is separable if and only if $K(\alpha) =K(\alpha^p)$ for all $\alpha \in L$

Struggling with a question on quotients in elementary Galois theory

How would I pronounce the symbol $[E:F]$?

Elements in extension field

Irreducible $f(x) \in F[x]$ of prime degree, $E/F$ finite extension, $p \mid [E:F]$.

Finding a primitive element for a field extension

Field Extensions Problem - From Paolo Aluffi's Book

Galois relations between subfields

$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?

How do extension fields implement $>, <$ comparisons?

I'm wondering definition of "E is a splitting over F"

An exponent of an element of a simple separable extension is contained in the base field.

$E/\mathbb F_q$ extension field. Show $[\mathbb F_q(\alpha) : \mathbb F_q]$ is smallest $n$ satisfying property.

A trace formula for an extension of complete valued fields

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