Question

Intermediate fields of a Galois extension

score 54 · Answer 1 · 2023-07-01 12:43:56

54

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Intermediate fields of a Galois extension

Published on 01 Jul 2023 - 12:43

score 117 · Answer 2 · 2023-07-03 14:59:56

117

Views

Is it true that $\mathbb{Q}(\sqrt{3}+\sqrt{5})= \mathbb{Q}(\sqrt{3+\sqrt{5}})$

Published on 03 Jul 2023 - 14:59

score 86 · Answer 3 · 2023-07-20 02:58:45

86

Views

Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. And find the elements of a finite field with 9 elements.

Published on 20 Jul 2023 - 2:58

score 292 · Answer 4 · 2023-07-22 08:51:23

292

Views

Splitting field of $X^2-2$

Published on 22 Jul 2023 - 8:51

score 64 · Answer 5 · 2023-07-30 11:01:49

64

Views

Galois group of $x^3+t^2x-t^3$ over $\mathbb{C}(t)$

Published on 30 Jul 2023 - 11:01

score 75 · Answer 6 · 2023-07-31 12:32:33

75

Views

Why is $\mathbb{Q}(\sqrt[8]{2},i)$ Galois over $\mathbb{Q}(i\sqrt{2})$?

Published on 31 Jul 2023 - 12:32

score 80 · Answer 7 · 2023-08-16 21:42:39

80

Views

Extension degree of the minimal splitting field of $X^4+2tX^2+t$ over $\mathbb{C}(t)$

Published on 16 Aug 2023 - 21:42

score 33 · Answer 8 · 2023-08-17 05:56:50

33

Views

linearly disjoint field extensions in terms of algebraic extension

Published on 17 Aug 2023 - 5:56

score 57 · Answer 9 · 2023-09-01 00:16:03

57

Views

How do I prove that the primitive element of a field extension are this way.

Published on 01 Sep 2023 - 0:16

score 100 · Answer 10 · 2023-09-20 07:31:19

100

Views

Splitting field and degree of extension of $x^4 + 2x^2 -2$ over $\mathbb F_{13}$

Published on 20 Sep 2023 - 7:31

score 69 · Answer 11 · 2023-10-06 15:54:01

69

Views

Set of all algebraic numbers A(C;Q) has no finite extension

Published on 06 Oct 2023 - 15:54

score 95 · Answer 12 · 2023-10-19 18:15:36

95

Views

Find the splitting field of $F = \{ x^{4}+1,x^{5}+2\}$ over $\mathbb Q$ and its extension-degree

Published on 19 Oct 2023 - 18:15

score 40 · Answer 13 · 2023-10-31 14:56:39

40

Views

Find Polynomial $P$ of a splitting field, such that deg($P$) matches $[L:K]$

Published on 31 Oct 2023 - 14:56

score 134 · Answer 14 · 2023-11-04 17:26:25

Splitting field of $ f(x) = x^4 - 2 $ over $ \Bbb{Q} $ with minimal Galois theory and avoiding the use of embedding in $ \Bbb{C} $.

score 31 · Answer 15 · 2023-11-06 11:34:10

31

Views

Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

Published on 06 Nov 2023 - 11:34

List Question

Intermediate fields of a Galois extension

Is it true that $\mathbb{Q}(\sqrt{3}+\sqrt{5})= \mathbb{Q}(\sqrt{3+\sqrt{5}})$

Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. And find the elements of a finite field with 9 elements.

Splitting field of $X^2-2$

Galois group of $x^3+t^2x-t^3$ over $\mathbb{C}(t)$

Why is $\mathbb{Q}(\sqrt[8]{2},i)$ Galois over $\mathbb{Q}(i\sqrt{2})$?

Extension degree of the minimal splitting field of $X^4+2tX^2+t$ over $\mathbb{C}(t)$

linearly disjoint field extensions in terms of algebraic extension

How do I prove that the primitive element of a field extension are this way.

Splitting field and degree of extension of $x^4 + 2x^2 -2$ over $\mathbb F_{13}$

Set of all algebraic numbers A(C;Q) has no finite extension

Find the splitting field of $F = \{ x^{4}+1,x^{5}+2\}$ over $\mathbb Q$ and its extension-degree

Find Polynomial $P$ of a splitting field, such that deg($P$) matches $[L:K]$

Splitting field of $ f(x) = x^4 - 2 $ over $ \Bbb{Q} $ with minimal Galois theory and avoiding the use of embedding in $ \Bbb{C} $.

Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

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