Question

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

score 250 · Answer 1 · 2016-09-11 13:54:45

250

Views

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Published on 11 Sep 2016 - 13:54

score 794 · Answer 2 · 2016-09-13 07:58:36

794

Views

Is there a relation between the polynomial that generates a splitting field and its minimal polynomial?

Published on 13 Sep 2016 - 7:58

score 73 · Answer 3 · 2016-09-18 17:06:30

73

Views

Splitting field for $x^2 + 1 \in \Bbb Q[x]$

Published on 18 Sep 2016 - 17:06

score 44 · Answer 4 · 2016-09-18 18:04:37

44

Views

For $f(x) = x^4 -x ^2 - 2 = (x^2-2)(x^2+1)$ in $\Bbb Q[x]$, show that $\Bbb Q(\sqrt{2}, i)$ is the splitting field.

Published on 18 Sep 2016 - 18:04

score 2.3k · Answer 5 · 2016-09-21 12:36:52

2.3k

Views

Showing that $x^p - a$ either splits or is irreducible for characteristic $p$ (prime) in a field F.

Published on 21 Sep 2016 - 12:36

score 999 · Answer 6 · 2016-09-24 13:24:43

999

Views

Separability and normal closure

Published on 24 Sep 2016 - 13:24

score 50 · Answer 7 · 2016-09-24 16:17:33

50

Views

Splitting field $\mathbb{Q}(\sqrt[11]{7},i)$

Published on 24 Sep 2016 - 16:17

score 1.5k · Answer 8 · 2016-09-27 12:44:37

1.5k

Views

Find a splitting field for $x^4 - x^2 - 2$ over $\Bbb Z_3$

Published on 27 Sep 2016 - 12:44

score 753 · Answer 9 · 2016-10-01 15:12:05

753

Views

Splitting Field Problem

Published on 01 Oct 2016 - 15:12

score 65 · Answer 10 · 2016-10-01 18:32:59

65

Views

Abstract algebra. splitting field

Published on 01 Oct 2016 - 18:32

score 618 · Answer 11 · 2016-10-09 07:25:02

618

Views

Galois group of a splitting field of a polynomial over $\mathbb{F}_7$

Published on 09 Oct 2016 - 7:25

score 179 · Answer 12 · 2016-10-14 01:11:19

179

Views

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Published on 14 Oct 2016 - 1:11

score 67 · Answer 13 · 2016-10-16 09:13:18

67

Views

Prove that $F=Z_3[x]/<x^2+x+2>$ is a splitting field for $f(x)=x^2+x+2$ over $Z_3$.

Published on 16 Oct 2016 - 9:13

score 54 · Answer 14 · 2016-10-18 21:53:08

54

Views

Multiplicative relations and roots in different splitting fields

Published on 18 Oct 2016 - 21:53

score 154 · Answer 15 · 2016-10-19 22:37:53

154

Views

If $M_1:K$ and $M_2:K$ are normal extensions then $K(M_1,M_2):K$ is normal.

Published on 19 Oct 2016 - 22:37

List Question

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Is there a relation between the polynomial that generates a splitting field and its minimal polynomial?

Splitting field for $x^2 + 1 \in \Bbb Q[x]$

For $f(x) = x^4 -x ^2 - 2 = (x^2-2)(x^2+1)$ in $\Bbb Q[x]$, show that $\Bbb Q(\sqrt{2}, i)$ is the splitting field.

Showing that $x^p - a$ either splits or is irreducible for characteristic $p$ (prime) in a field F.

Separability and normal closure

Splitting field $\mathbb{Q}(\sqrt[11]{7},i)$

Find a splitting field for $x^4 - x^2 - 2$ over $\Bbb Z_3$

Splitting Field Problem

Abstract algebra. splitting field

Galois group of a splitting field of a polynomial over $\mathbb{F}_7$

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Prove that $F=Z_3[x]/<x^2+x+2>$ is a splitting field for $f(x)=x^2+x+2$ over $Z_3$.

Multiplicative relations and roots in different splitting fields

If $M_1:K$ and $M_2:K$ are normal extensions then $K(M_1,M_2):K$ is normal.

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