List questions from splitting-field

Published on 22 May 2020 - 20:00

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Splitting field $L$ of polynomial $f \in K[x]$ with degree $n$ satisfies $[L:K] | n!$

Published on 23 May 2020 - 19:24

59

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Confusion Over Polynomial Separability Example

Published on 27 May 2020 - 17:35

49

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Find splitting field of $(x^3-x^2-x)(x^4-x^2+1)$ over $\mathbb{F}_3$

Published on 27 May 2020 - 22:13

36

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Why do we have $Q(\alpha, z) = \mathbb{Q}(\alpha, z, \overline{z})$ where $\alpha, z, \overline{z}$ are the roots of $X^3+X+1 \in \mathbb{Q}[x]$?

Published on 28 May 2020 - 12:43

74

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Primitive third root of the unit

Published on 31 May 2020 - 23:13

34

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Determine degree min. polynomial

Published on 02 Jun 2020 - 14:43

115

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Two candidates for definition of splitting field

Published on 06 Jun 2020 - 17:04

148

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Find a splitting field and its Galois group

Published on 07 Jun 2020 - 3:01

132

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Find the splitting field of $x^3 + 4$ over $\mathbb{Q}$

Published on 08 Jun 2020 - 4:13

33

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Find splitting field and irreducible decomposition

Published on 08 Jun 2020 - 10:16

101

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Find decomposition of $x^8 -1$ over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_4$

Published on 10 Jun 2020 - 13:28

47

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Checking if there is some square root of an element over an extension of the field of 5-adic numbers

Published on 11 Jun 2020 - 20:25

76

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Algorithm to determine splitting field of polynomial?

Published on 14 Jun 2020 - 14:35

59

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If $L$ is the splitting field of a polynomial $f$ over $K$, $r \in M \supset L$ any element. Is $L[r]$ the splitting field of $f$ over $K[r]$?

Published on 14 Jun 2020 - 20:47

List Question

Dummit & Foote 14.4.4

Splitting field $L$ of polynomial $f \in K[x]$ with degree $n$ satisfies $[L:K] | n!$

Confusion Over Polynomial Separability Example

Find splitting field of $(x^3-x^2-x)(x^4-x^2+1)$ over $\mathbb{F}_3$

Why do we have $Q(\alpha, z) = \mathbb{Q}(\alpha, z, \overline{z})$ where $\alpha, z, \overline{z}$ are the roots of $X^3+X+1 \in \mathbb{Q}[x]$?

Primitive third root of the unit

Determine degree min. polynomial

Two candidates for definition of splitting field

Find a splitting field and its Galois group

Find the splitting field of $x^3 + 4$ over $\mathbb{Q}$

Find splitting field and irreducible decomposition

Find decomposition of $x^8 -1$ over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_4$

Checking if there is some square root of an element over an extension of the field of 5-adic numbers

Algorithm to determine splitting field of polynomial?

If $L$ is the splitting field of a polynomial $f$ over $K$, $r \in M \supset L$ any element. Is $L[r]$ the splitting field of $f$ over $K[r]$?

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