List questions from splitting-field

Published on 10 Apr 2026 - 9:58

142

Views

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Published on 22 Apr 2026 - 23:25

49

Views

Does $x^3-x+3$ have any roots in $\mathbb{F}_5$?

Published on 16 Apr 2026 - 1:53

604

Views

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

Published on 14 Apr 2026 - 23:40

701

Views

Proving a Galois Group is isomorphic to $D_4$

Published on 15 Apr 2026 - 14:18

395

Views

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Published on 01 May 2026 - 8:37

503

Views

Galois group as permutations of roots

Published on 17 Apr 2026 - 10:36

58

Views

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Published on 16 Apr 2026 - 11:53

368

Views

Degree of splitting field of $x^6+tx^3+t$ in $\mathbb{F}_3(t)[x]$

Published on 15 Apr 2026 - 19:18

597

Views

A question on the definition of splitting field

Published on 10 Apr 2026 - 15:08

191

Views

Adjoining square root of a discriminant

Published on 12 Apr 2026 - 14:13

202

Views

If $E= \mathbb{Q}(\sqrt{2} + \sqrt{7})$ Show that $E/\mathbb{Q}$ is a Galois Extension.

Published on 17 Apr 2026 - 7:17

367

Views

Field extension roots of unity

Published on 13 Apr 2026 - 13:21

199

Views

Splitting field of $x^2+[1]$ over $\mathbb Z_2$

Published on 12 Apr 2026 - 14:49

80

Views

Algebraic closure of a real-closed field

Published on 15 Apr 2026 - 14:37

List Question

Splitting field construction

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Does $x^3-x+3$ have any roots in $\mathbb{F}_5$?

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

Proving a Galois Group is isomorphic to $D_4$

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Galois group as permutations of roots

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Degree of splitting field of $x^6+tx^3+t$ in $\mathbb{F}_3(t)[x]$

A question on the definition of splitting field

Adjoining square root of a discriminant

If $E= \mathbb{Q}(\sqrt{2} + \sqrt{7})$ Show that $E/\mathbb{Q}$ is a Galois Extension.

Field extension roots of unity

Splitting field of $x^2+[1]$ over $\mathbb Z_2$

Algebraic closure of a real-closed field

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