List questions from splitting-field

Published on 11 Feb 2019 - 6:24

115

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Splitting Fields over arbitrary fields

Published on 15 Feb 2019 - 13:34

505

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Degree of splitting field for $f(x) = x^4 - x^2 + 4$ over $\mathbb{Q}$

Published on 18 Feb 2019 - 2:50

64

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Is $[\Bbb Q(5^{1/2}, 5^{1/7}): \Bbb Q(5^{1/7})]$ a normal extension?

Published on 20 Feb 2019 - 23:05

358

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Can splitting field be generated by one root?

Published on 24 Feb 2019 - 12:02

1.4k

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Splitting field of separable polynomial is Galois extension

Published on 24 Feb 2019 - 13:38

1k

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$f(x)$ is irreducible over finite field $F_p$ , does $f(x)$ split over $F_p / \langle f(x) \rangle$?

Published on 26 Feb 2019 - 20:37

58

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Algebraic closure not even finitely generated over base field

Published on 28 Feb 2019 - 22:20

1.8k

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Degree of splitting field of $X^n-1$ over some finite field

Published on 02 Mar 2019 - 16:55

186

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Dimension of splitting field as the order of an element mod n

Published on 03 Mar 2019 - 16:00

138

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automorphism group of splitting field of cubic polynomial over $\mathbb{Q}$

Published on 04 Mar 2019 - 21:45

457

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Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

Published on 06 Mar 2019 - 16:03

666

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Did I find the splitting field of $x^3-3x+1$ over $\Bbb Q$?

Published on 09 Mar 2019 - 15:08

110

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Extension of Splitting Fields over An Arbitrary Field

Published on 14 Mar 2019 - 1:38

100

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If $f(x) \in\Bbb Q[x]$ has splitting field of degree $16$ over $\Bbb Q$ is $f(x)$ solvable by radicals?

Published on 24 Mar 2026 - 22:01

List Question

(Degree of) Splitting Field for $f(x) = x^p - 2$ over $\mathbb{Q}$, p prime

Splitting Fields over arbitrary fields

Degree of splitting field for $f(x) = x^4 - x^2 + 4$ over $\mathbb{Q}$

Is $[\Bbb Q(5^{1/2}, 5^{1/7}): \Bbb Q(5^{1/7})]$ a normal extension?

Can splitting field be generated by one root?

Splitting field of separable polynomial is Galois extension

$f(x)$ is irreducible over finite field $F_p$ , does $f(x)$ split over $F_p / \langle f(x) \rangle$?

Algebraic closure not even finitely generated over base field

Degree of splitting field of $X^n-1$ over some finite field

Dimension of splitting field as the order of an element mod n

automorphism group of splitting field of cubic polynomial over $\mathbb{Q}$

Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

Did I find the splitting field of $x^3-3x+1$ over $\Bbb Q$?

Extension of Splitting Fields over An Arbitrary Field

If $f(x) \in\Bbb Q[x]$ has splitting field of degree $16$ over $\Bbb Q$ is $f(x)$ solvable by radicals?

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