List questions from splitting-field

Published on 20 Mar 2016 - 19:11

369

Views

$K \subset E \subset L$ finite field extensions and $L$ normal over $K$. Is $L$ normal over $E$, and is $E$ normal over $K$?

Published on 29 Mar 2016 - 12:52

364

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Normal closure $L$ of $\mathbb{Q}(\sqrt[4]{7})$ and structure of $Gal(L/\mathbb{Q})$

Published on 29 Mar 2016 - 18:55

89

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Find $\mathrm{Gal}(L, \mathbb{Q})$ and prove that $\sqrt[3]{3} \in L$

Published on 08 Apr 2016 - 16:30

153

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Normal closure $L$ of $K=\mathbb{Q}(\sqrt{10+3\sqrt{13}})$ and structure of $\mathrm{Gal}(L/\mathbb{Q})$

Published on 08 Apr 2016 - 16:58

643

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Splitting field for $x^4-x^2-2$

Published on 11 Apr 2016 - 22:33

2.5k

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

Published on 11 Apr 2016 - 23:29

47

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If every polynomial in $F[x]$ splits then there exists no nontrivial algebraic extension

Published on 12 Apr 2016 - 16:53

570

Views

Normal closure of $\mathbb{Q}(\sqrt{11+3\sqrt{13}})$ over $\mathbb{Q}$

Published on 13 Apr 2016 - 10:42

451

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Minimal polynomial for $\alpha=\sqrt{3-2\sqrt{2}}$ over $\mathbb{Q}$

Published on 13 Apr 2016 - 11:14

119

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Proving an element belongs to field extension

Published on 13 Apr 2016 - 12:07

57

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Degree of field extensions

Published on 13 Apr 2016 - 16:02

2.2k

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Splitting field of $x^5-3x^3+x^2-3$

Published on 16 Apr 2016 - 0:20

296

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Splitting field of an irreducible polynomial of degree four

Published on 18 Apr 2016 - 9:16

1.1k

Views

Galois group of splitting field over $\mathbb{Q}$

Published on 19 Apr 2016 - 1:03

List Question

Find the splitting field without the explicit roots

$K \subset E \subset L$ finite field extensions and $L$ normal over $K$. Is $L$ normal over $E$, and is $E$ normal over $K$?

Normal closure $L$ of $\mathbb{Q}(\sqrt[4]{7})$ and structure of $Gal(L/\mathbb{Q})$

Find $\mathrm{Gal}(L, \mathbb{Q})$ and prove that $\sqrt[3]{3} \in L$

Normal closure $L$ of $K=\mathbb{Q}(\sqrt{10+3\sqrt{13}})$ and structure of $\mathrm{Gal}(L/\mathbb{Q})$

Splitting field for $x^4-x^2-2$

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

If every polynomial in $F[x]$ splits then there exists no nontrivial algebraic extension

Normal closure of $\mathbb{Q}(\sqrt{11+3\sqrt{13}})$ over $\mathbb{Q}$

Minimal polynomial for $\alpha=\sqrt{3-2\sqrt{2}}$ over $\mathbb{Q}$

Proving an element belongs to field extension

Degree of field extensions

Splitting field of $x^5-3x^3+x^2-3$

Splitting field of an irreducible polynomial of degree four

Galois group of splitting field over $\mathbb{Q}$

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