Question

What fields are isomorphic to $\mathbb{Q}[\sqrt{2}]$ other than $\mathbb{Q}[\sqrt{2}]$ itself?

score 964 · Answer 1 · 2017-07-06 18:39:00

964

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What fields are isomorphic to $\mathbb{Q}[\sqrt{2}]$ other than $\mathbb{Q}[\sqrt{2}]$ itself?

Published on 06 Jul 2017 - 18:39

score 175 · Answer 2 · 2017-07-11 14:30:54

175

Views

Cardinality Splitting field of $\varphi = X^5+2X^4+X^3+X^2+X+2 \in \mathbb F_3 [X]$

Published on 11 Jul 2017 - 14:30

score 707 · Answer 3 · 2017-07-11 22:38:33

707

Views

How to get the splitting field of a polynomial?

Published on 11 Jul 2017 - 22:38

score 80 · Answer 4 · 2017-07-20 15:11:36

80

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Prove that there is no polynomial of a given degree whose splitting field is a given Galois extenstion

Published on 20 Jul 2017 - 15:11

score 55 · Answer 5 · 2017-07-28 17:25:00

55

Views

About splitting fields

Published on 28 Jul 2017 - 17:25

score 1.2k · Answer 6 · 2017-08-02 01:57:28

1.2k

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Finding minimal polynomial and splitting field

Published on 02 Aug 2017 - 1:57

score 13.6k · Answer 7 · 2017-08-11 09:38:23

13.6k

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Find the splitting field of $x^4+1$ over $\mathbb Q$.

Published on 11 Aug 2017 - 9:38

score 150 · Answer 8 · 2017-08-17 02:37:19

150

Views

Dimension of a splitting field over a field $K$

Published on 17 Aug 2017 - 2:37

score 121 · Answer 9 · 2017-08-17 19:52:22

121

Views

In which of the cases is the field $F$ the splitting field of some polynomial $f \in \mathbb{Q}[x]$ over $\mathbb{Q}$?

Published on 17 Aug 2017 - 19:52

score 609 · Answer 10 · 2017-08-22 23:08:14

609

Views

Prove that the splitting field is not an algebraic closure

Published on 22 Aug 2017 - 23:08

score 41 · Answer 11 · 2017-09-12 06:16:39

41

Views

Finding splitting field over $\mathbb Q$

Published on 12 Sep 2017 - 6:16

score 288 · Answer 12 · 2017-09-13 14:25:49

288

Views

Degree of splitting field over $\mathbb Q$

Published on 13 Sep 2017 - 14:25

score 107 · Answer 13 · 2026-02-23 02:46:05

107

Views

Is there a polynomial over $\mathbb{Q}$ which $K$ is its splitting field.

Published on 23 Feb 2026 - 2:46

score 578 · Answer 14 · 2017-09-16 09:41:16

578

Views

Find the degree of splitting field of $x^3-x+1$ over $\mathbb{F_3}$

Published on 16 Sep 2017 - 9:41

score 44 · Answer 15 · 2017-09-21 20:55:36

44

Views

For the following polynomials (a) $f(x)=x^4-5x^2+6, F = \mathbb{Z}_7$, (b) $f(x)=x^3-3 , F=\mathbb{Q}$ in the given field $F$ find:

Published on 21 Sep 2017 - 20:55

List Question

What fields are isomorphic to $\mathbb{Q}[\sqrt{2}]$ other than $\mathbb{Q}[\sqrt{2}]$ itself?

Cardinality Splitting field of $\varphi = X^5+2X^4+X^3+X^2+X+2 \in \mathbb F_3 [X]$

How to get the splitting field of a polynomial?

Prove that there is no polynomial of a given degree whose splitting field is a given Galois extenstion

About splitting fields

Finding minimal polynomial and splitting field

Find the splitting field of $x^4+1$ over $\mathbb Q$.

Dimension of a splitting field over a field $K$

In which of the cases is the field $F$ the splitting field of some polynomial $f \in \mathbb{Q}[x]$ over $\mathbb{Q}$?

Prove that the splitting field is not an algebraic closure

Finding splitting field over $\mathbb Q$

Degree of splitting field over $\mathbb Q$

Is there a polynomial over $\mathbb{Q}$ which $K$ is its splitting field.

Find the degree of splitting field of $x^3-x+1$ over $\mathbb{F_3}$

For the following polynomials (a) $f(x)=x^4-5x^2+6, F = \mathbb{Z}_7$, (b) $f(x)=x^3-3 , F=\mathbb{Q}$ in the given field $F$ find:

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