List questions from splitting-field

Published on 22 Mar 2026 - 16:09

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splitting field of $X^{4} -42$ over $\mathbb{Q}$

Published on 22 Mar 2026 - 8:04

407

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Find the degree of splitting field of a separable polynomial over finite field

Published on 20 Mar 2026 - 2:57

77

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If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

Published on 22 Mar 2026 - 10:22

329

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When a product of two primitive elements is also primitive?

Published on 21 Mar 2026 - 8:35

86

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Is linear disjunction a polynomial condition?

Published on 24 Mar 2026 - 23:30

89

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Computing dimension of the splitting field.

Published on 20 Mar 2026 - 1:08

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Let $f,g$ be two irreducible polynomials over finite field $\mathbb{F}_q$ such that $\text{ord}(f)=\text{ord}(g)$. Prove that $\deg(f)=\deg(g)$.

Published on 22 Mar 2026 - 3:44

108

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Which primes are ramified?

Published on 17 Mar 2026 - 4:11

90

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How to find $\operatorname{Gal}(S/\mathbb{Q})$

Published on 20 Mar 2026 - 6:37

824

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Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$

Published on 20 Mar 2026 - 6:55

820

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Proof verification: The degree of a splitting field of a polynomial $f$ divides deg($f$) factorial

Published on 24 Mar 2026 - 22:16

360

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The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

Published on 25 Mar 2026 - 1:17

267

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Is $-1$ sum of squares in the field $\mathbb{Q(\beta)}$ where $\beta = 2^{1/3}e^{2\pi i /3}$

Published on 20 Mar 2026 - 4:21

1.1k

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basis for the splitting field of $x^3 - 3$ over the rationals

Published on 25 Mar 2026 - 1:17

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Non-galois real extensions of $\mathbb Q$

splitting field of $X^{4} -42$ over $\mathbb{Q}$

Find the degree of splitting field of a separable polynomial over finite field

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

When a product of two primitive elements is also primitive?

Is linear disjunction a polynomial condition?

Computing dimension of the splitting field.

Let $f,g$ be two irreducible polynomials over finite field $\mathbb{F}_q$ such that $\text{ord}(f)=\text{ord}(g)$. Prove that $\deg(f)=\deg(g)$.

Which primes are ramified?

How to find $\operatorname{Gal}(S/\mathbb{Q})$

Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$

Proof verification: The degree of a splitting field of a polynomial $f$ divides deg($f$) factorial

The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

Is $-1$ sum of squares in the field $\mathbb{Q(\beta)}$ where $\beta = 2^{1/3}e^{2\pi i /3}$

basis for the splitting field of $x^3 - 3$ over the rationals

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