Question

How to prove an element doesn't belongs to a splitting field?

score 43 · Answer 1 · 2020-04-25 19:03:23

43

Views

How to prove an element doesn't belongs to a splitting field?

Published on 25 Apr 2020 - 19:03

score 645 · Answer 2 · 2020-05-01 16:16:43

645

Views

Galois group of splitting field of $X^4-6X^2+7$ is non-abelian

Published on 01 May 2020 - 16:16

score 671 · Answer 3 · 2020-05-02 06:46:32

671

Views

The galois group of polynomial ($x^5-3$) over $\mathbb{Q}$

Published on 02 May 2020 - 6:46

score 310 · Answer 4 · 2020-05-02 16:17:13

310

Views

The automorphism of splitting field of x^p-x+a over Z_p.

Published on 02 May 2020 - 16:17

score 69 · Answer 5 · 2020-05-05 03:09:45

69

Views

Splitting field over Z_2

Published on 05 May 2020 - 3:09

score 113 · Answer 6 · 2020-05-05 20:52:33

113

Views

How do I find _all_ the roots of $f$ in $F_{27}$ hence show that $f$ splits in $F_{27}$

Published on 05 May 2020 - 20:52

score 77 · Answer 7 · 2020-05-05 22:46:00

77

Views

T/F: If $f(x), g(x) \in \mathbb{Q}[x]$ are irreducible polynomials that have the same splitting field, then deg $f=$ deg $g$.

Published on 05 May 2020 - 22:46

score 172 · Answer 8 · 2020-05-07 13:12:53

172

Views

Subfields of splitting field of $x^{15}-1$ over $\mathbb Q$

Published on 07 May 2020 - 13:12

score 83 · Answer 9 · 2020-05-08 13:08:22

83

Views

The Galois group of the splitting field for $\prod{(X^{p_i}-1)}$ over $\mathbb{Q}$

Published on 08 May 2020 - 13:08

score 504 · Answer 10 · 2020-05-12 04:42:17

504

Views

Simple Field Extensions from a Separable Element and an Arbitrary Element

Published on 12 May 2020 - 4:42

score 514 · Answer 11 · 2020-05-12 08:45:29

514

Views

Let $K = \mathbb{Q}(\sqrt{p_1},\sqrt{p_2},\dots,\sqrt{p_n})$ for distinct primes $p_1,p_2,\dots,p_n$. Prove $[K:\mathbb{Q}] = 2^n$.

Published on 12 May 2020 - 8:45

score 170 · Answer 12 · 2020-05-12 22:17:29

170

Views

Prove that $f(x)$ is irreducible over $\mathbb{Q}$

Published on 12 May 2020 - 22:17

score 156 · Answer 13 · 2020-05-13 21:24:07

156

Views

Can there exist a finite extension $K$ where $K$ is Galois over $\mathbb Q(i)$ but $K$ is not Galois over $\mathbb Q?$

Published on 13 May 2020 - 21:24

score 65 · Answer 14 · 2020-05-19 04:30:43

65

Views

Find basis of $\mathbb Q(\sqrt[3]{2},\sqrt{-3})$ over the field $\mathbb Q(\sqrt[3]{2}\omega)$.

Published on 19 May 2020 - 4:30

score 74 · Answer 15 · 2020-05-20 00:58:22

74

Views

If $K(\zeta,\beta)/K$ is the splitting field for $f$, what can we say about $K(\zeta,\beta)/K(\zeta)$?

Published on 20 May 2020 - 0:58

List Question

How to prove an element doesn't belongs to a splitting field?

Galois group of splitting field of $X^4-6X^2+7$ is non-abelian

The galois group of polynomial ($x^5-3$) over $\mathbb{Q}$

The automorphism of splitting field of x^p-x+a over Z_p.

Splitting field over Z_2

How do I find _all_ the roots of $f$ in $F_{27}$ hence show that $f$ splits in $F_{27}$

T/F: If $f(x), g(x) \in \mathbb{Q}[x]$ are irreducible polynomials that have the same splitting field, then deg $f=$ deg $g$.

Subfields of splitting field of $x^{15}-1$ over $\mathbb Q$

The Galois group of the splitting field for $\prod{(X^{p_i}-1)}$ over $\mathbb{Q}$

Simple Field Extensions from a Separable Element and an Arbitrary Element

Let $K = \mathbb{Q}(\sqrt{p_1},\sqrt{p_2},\dots,\sqrt{p_n})$ for distinct primes $p_1,p_2,\dots,p_n$. Prove $[K:\mathbb{Q}] = 2^n$.

Prove that $f(x)$ is irreducible over $\mathbb{Q}$

Can there exist a finite extension $K$ where $K$ is Galois over $\mathbb Q(i)$ but $K$ is not Galois over $\mathbb Q?$

Find basis of $\mathbb Q(\sqrt[3]{2},\sqrt{-3})$ over the field $\mathbb Q(\sqrt[3]{2}\omega)$.

If $K(\zeta,\beta)/K$ is the splitting field for $f$, what can we say about $K(\zeta,\beta)/K(\zeta)$?

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