List questions from separable-extension

Published on 09 Apr 2026 - 6:23

63

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When is it true that $K \cap F(a) = F$ and $[K(a):F(a)] = [K:F]$?

Published on 09 Apr 2026 - 6:20

45

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Unable to understand an argument in proof of theorem of Hungerford Algebra Ch - Fields and Galois Theory

Published on 23 Feb 2026 - 6:41

80

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An argument in Galois Theory notes about which i have no idea

Published on 23 Feb 2026 - 6:38

110

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Need help in deducing 2 arguments related to separable extension

Published on 23 Feb 2026 - 6:36

98

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Finite Purely Inseparable Extension

Published on 23 Feb 2026 - 6:34

434

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Does an algebraically closed field contain all algebraic field extensions?

Published on 23 Feb 2026 - 6:42

808

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Is a separable extension of an extension field also a separable extension of the base/ground field?

Published on 23 Feb 2026 - 6:40

59

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Separable extension of $k \subset K \subset L$

Published on 23 Feb 2026 - 6:36

644

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Finding the fixed subfield of an automorphism subgroup of $k(x)$.

Published on 23 Feb 2026 - 6:39

306

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Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

Published on 23 Feb 2026 - 6:40

593

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Degree of separability equals degree of separable closure

Published on 23 Feb 2026 - 6:38

118

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If $K = F(\alpha)$ is a non separable and finite extension, then $T^K_F = 0$

Published on 23 Feb 2026 - 6:40

236

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Let $K$ be a separable extension of $F$.

Published on 23 Feb 2026 - 6:37

419

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Finite extension of a characteristic p field is separable if and only if $E=F(E^p)$

Published on 23 Feb 2026 - 6:38

List Question

A generalization of the theorem on natural irrationalities?

When is it true that $K \cap F(a) = F$ and $[K(a):F(a)] = [K:F]$?

Unable to understand an argument in proof of theorem of Hungerford Algebra Ch - Fields and Galois Theory

An argument in Galois Theory notes about which i have no idea

Need help in deducing 2 arguments related to separable extension

Finite Purely Inseparable Extension

Does an algebraically closed field contain all algebraic field extensions?

Is a separable extension of an extension field also a separable extension of the base/ground field?

Separable extension of $k \subset K \subset L$

Finding the fixed subfield of an automorphism subgroup of $k(x)$.

Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

Degree of separability equals degree of separable closure

If $K = F(\alpha)$ is a non separable and finite extension, then $T^K_F = 0$

Let $K$ be a separable extension of $F$.

Finite extension of a characteristic p field is separable if and only if $E=F(E^p)$

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