List questions from galois-theory

Published on 28 Mar 2018 - 22:37

61

Views

Polynomial divibility over finite field

Published on 25 Mar 2026 - 3:18

602

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Proving $Gal(K/\mathbb{Q})$ is $D_4$.

Published on 25 Mar 2026 - 9:47

699

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Proving a Galois Group is isomorphic to $D_4$

Published on 25 Mar 2026 - 9:48

127

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Condition for Being Galois

Published on 25 Mar 2026 - 1:21

240

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Is the field extension $\mathbb{Q}(\sqrt{5 + \sqrt{7}})$ over $\mathbb{Q}$ a Galois extension?

Published on 01 Apr 2018 - 0:34

51

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A little confusion on galois groups

Published on 01 Apr 2018 - 7:15

266

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Let $f \in F[x]$, then discriminant of $f$ lies in $F$.

Published on 24 Mar 2026 - 17:31

67

Views

If the Sums of all $k$-th Powers are Equal then the Terms are Equal

Published on 02 Apr 2018 - 18:47

65

Views

$\mathbb{Q}(3^{1/n},e^{2i\pi/n})$ is not contained in any cyclotomic extension

Published on 20 Mar 2026 - 8:13

339

Views

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

Published on 25 Mar 2026 - 10:57

57

Views

Refrence Request - Galois's Memoir

Published on 04 Apr 2018 - 14:33

74

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Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

Published on 25 Mar 2026 - 10:57

449

Views

Decomposing an abelian extension into cyclic extensions

Published on 25 Mar 2026 - 6:00

167

Views

Show that $[k(t): k(t^4 + t) ] = 4$

Published on 22 Mar 2026 - 7:12

List Question

On a characterization of a field monomorphism

Polynomial divibility over finite field

Proving $Gal(K/\mathbb{Q})$ is $D_4$.

Proving a Galois Group is isomorphic to $D_4$

Condition for Being Galois

Is the field extension $\mathbb{Q}(\sqrt{5 + \sqrt{7}})$ over $\mathbb{Q}$ a Galois extension?

A little confusion on galois groups

Let $f \in F[x]$, then discriminant of $f$ lies in $F$.

If the Sums of all $k$-th Powers are Equal then the Terms are Equal

$\mathbb{Q}(3^{1/n},e^{2i\pi/n})$ is not contained in any cyclotomic extension

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

Refrence Request - Galois's Memoir

Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

Decomposing an abelian extension into cyclic extensions

Show that $[k(t): k(t^4 + t) ] = 4$

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