List questions from separable-extension

Published on 23 Feb 2026 - 4:55

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Irreducible polynomial of the form $x^4+ax^2+b \in K[x]$, where $K$ is a field with char$K \neq 2$, is separable?

Published on 23 Feb 2026 - 4:58

75

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If $L/K$ is a finite separable extension and $P \in K[X], Q \in L[X]$, then $P = Q^n \Rightarrow Q \in K[X]$

Published on 23 Feb 2026 - 4:58

106

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Is the splitting field of $x^7+x^5+x^2+1$ over the field $F$ with 25 elements a separable extension?

Published on 23 Feb 2026 - 4:59

258

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Show that every non-constant polynomial $f(x)\in K[x]$ is separable.

Published on 23 Feb 2026 - 4:56

3.6k

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Why every extension of a characteristic zero field is separable?

Published on 23 Feb 2026 - 4:55

124

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Showing equivalence of Two definitions for separable extensions

Published on 23 Feb 2026 - 4:55

152

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largest purely inseparable extension (Serre, Local algebra p.46)

Published on 23 Feb 2026 - 4:53

144

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Maximal subfields of a commutative algebra

Published on 23 Feb 2026 - 4:52

75

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Possible degrees of separable irreducible polynomials

Published on 23 Feb 2026 - 4:53

1k

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Separable extension and tensor product

Published on 23 Feb 2026 - 4:50

18

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$[F(a):F(a^i)](y_1+...+y_m)=x_1^i+...+x_n^i$

Published on 23 Feb 2026 - 4:57

230

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Lang's definition of separability (solved)

Published on 23 Feb 2026 - 4:53

332

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Tower of separable field extensions is separable

Published on 23 Feb 2026 - 4:52

136

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Degree of normal closure

Published on 05 Apr 2026 - 16:06

List Question

Finite dimensional field extension of Q simple

Irreducible polynomial of the form $x^4+ax^2+b \in K[x]$, where $K$ is a field with char$K \neq 2$, is separable?

If $L/K$ is a finite separable extension and $P \in K[X], Q \in L[X]$, then $P = Q^n \Rightarrow Q \in K[X]$

Is the splitting field of $x^7+x^5+x^2+1$ over the field $F$ with 25 elements a separable extension?

Show that every non-constant polynomial $f(x)\in K[x]$ is separable.

Why every extension of a characteristic zero field is separable?

Showing equivalence of Two definitions for separable extensions

largest purely inseparable extension (Serre, Local algebra p.46)

Maximal subfields of a commutative algebra

Possible degrees of separable irreducible polynomials

Separable extension and tensor product

$[F(a):F(a^i)](y_1+...+y_m)=x_1^i+...+x_n^i$

Lang's definition of separability (solved)

Tower of separable field extensions is separable

Degree of normal closure

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