Question

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

score 54 · Answer 1 · 2023-11-06 12:39:52

54

Views

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Published on 06 Nov 2023 - 12:39

score 107 · Answer 2 · 2023-11-09 23:01:48

107

Views

Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

Published on 09 Nov 2023 - 23:01

score 43 · Answer 3 · 2023-11-16 21:11:42

43

Views

Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Published on 16 Nov 2023 - 21:11

score 35 · Answer 4 · 2023-12-03 15:11:09

35

Views

Question about the degree of the splitting field of $X^4-2X^2-2$

Published on 03 Dec 2023 - 15:11

score 61 · Answer 5 · 2023-12-04 12:09:01

61

Views

$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

Published on 04 Dec 2023 - 12:09

score 67 · Answer 6 · 2023-12-04 15:23:27

67

Views

An exercise where I need to prove that a field extension is normal

Published on 04 Dec 2023 - 15:23

score 108 · Answer 7 · 2023-12-05 11:36:06

108

Views

Exercises on the field extension $E := \mathbb{F}_3[X]/(X^2 + X + 2)$

Published on 05 Dec 2023 - 11:36

score 86 · Answer 8 · 2023-12-05 15:53:55

86

Views

$K$-automorphisms permuting the roots of $f$ in $L$.

Published on 05 Dec 2023 - 15:53

score 47 · Answer 9 · 2023-12-07 15:25:20

47

Views

Some exercises about field extensions and galois groups

Published on 07 Dec 2023 - 15:25

score 59 · Answer 10 · 2023-12-08 20:32:28

59

Views

Computing the Galois group of polynomials of high degree

Published on 08 Dec 2023 - 20:32

score 88 · Answer 11 · 2023-12-11 11:52:24

88

Views

Show that $K( \frac{X^3}{X^2+1} ) ⊂ K(X)$ is an algebraic extension and find the galois group

Published on 11 Dec 2023 - 11:52

score 39 · Answer 12 · 2023-12-11 13:25:01

39

Views

Splitting field and Galois group of $f := x^4 + x^3 + x^2 + x + 1 ∈ \mathbb{Q}[X]$

Published on 11 Dec 2023 - 13:25

score 151 · Answer 13 · 2023-12-23 11:21:41

151

Views

Representing finite fields

Published on 23 Dec 2023 - 11:21

score 64 · Answer 14 · 2024-01-04 13:49:49

64

Views

Galois Group of $X^3-a $ in different cases

Published on 04 Jan 2024 - 13:49

score 65 · Answer 15 · 2024-01-18 22:03:32

65

Views

Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

Published on 18 Jan 2024 - 22:03

List Question

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Question about the degree of the splitting field of $X^4-2X^2-2$

$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

An exercise where I need to prove that a field extension is normal

Exercises on the field extension $E := \mathbb{F}_3[X]/(X^2 + X + 2)$

$K$-automorphisms permuting the roots of $f$ in $L$.

Some exercises about field extensions and galois groups

Computing the Galois group of polynomials of high degree

Show that $K( \frac{X^3}{X^2+1} ) ⊂ K(X)$ is an algebraic extension and find the galois group

Splitting field and Galois group of $f := x^4 + x^3 + x^2 + x + 1 ∈ \mathbb{Q}[X]$

Representing finite fields

Galois Group of $X^3-a $ in different cases

Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

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