List questions from splitting-field

Published on 18 Oct 2019 - 4:12

27

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the roots of $T^n -a$ in a splitting field.

Published on 22 Oct 2019 - 21:48

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

3.6k

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Why every extension of a characteristic zero field is separable?

Published on 23 Feb 2026 - 4:55

48

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Finding primitive element of an extension

Published on 07 Nov 2019 - 16:55

106

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Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

Published on 23 Feb 2026 - 1:04

45

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What polynomial in $\mathbb{F}_{p^m}[x]$ has splitting field $\mathbb{F}_{p^n}$?

Published on 20 Nov 2019 - 7:13

38

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Several roots in one field extension?

Published on 22 Nov 2019 - 12:41

958

Views

Is $\mathbb{Q}(\sqrt{2}, 2^{1/3})$ a Galois extension of $\mathbb{Q}$?

Published on 26 Nov 2019 - 1:03

123

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Splitting field $L$ of $f(x)=x^6-9x^4+3x^2+5$ over $\mathbb{Q}[x]$ and the degree of the extension $[L:\mathbb{Q}]$

Published on 09 Dec 2019 - 0:01

84

Views

Galois Theory and splitting field

Published on 10 Dec 2019 - 16:18

36

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Splitting Fields - Field Extensions

Published on 11 Dec 2019 - 8:09

117

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Explanation about a theorem from Basic Algebra I, Jacobson

Published on 12 Dec 2019 - 23:30

489

Views

Splitting field of $x^4 + 4$ over $\mathbb{Q}$

Published on 17 Dec 2019 - 3:28

38

Views

Splitting fields of $F$-algebra $F[X]/(P(X))$.

Published on 17 Dec 2019 - 4:06

List Question

Looking for the splitting field of polynomials over $\mathbb{F}_4$

the roots of $T^n -a$ in a splitting field.

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

Why every extension of a characteristic zero field is separable?

Finding primitive element of an extension

Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

What polynomial in $\mathbb{F}_{p^m}[x]$ has splitting field $\mathbb{F}_{p^n}$?

Several roots in one field extension?

Is $\mathbb{Q}(\sqrt{2}, 2^{1/3})$ a Galois extension of $\mathbb{Q}$?

Splitting field $L$ of $f(x)=x^6-9x^4+3x^2+5$ over $\mathbb{Q}[x]$ and the degree of the extension $[L:\mathbb{Q}]$

Galois Theory and splitting field

Splitting Fields - Field Extensions

Explanation about a theorem from Basic Algebra I, Jacobson

Splitting field of $x^4 + 4$ over $\mathbb{Q}$

Splitting fields of $F$-algebra $F[X]/(P(X))$.

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