Question

Galois Extensions and Splitting Fields of Separable Polynomials

score 149 · Answer 1 · 2026-03-26 16:11:15

149

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Galois Extensions and Splitting Fields of Separable Polynomials

Published on 26 Mar 2026 - 16:11

score 49 · Answer 2 · 2026-03-25 23:38:19

49

Views

How to find the minimal basis of an invariant ring?

Published on 25 Mar 2026 - 23:38

score 42 · Answer 3 · 2026-04-04 11:56:33

42

Views

Condition for Intermediate Field to be Galois

Published on 04 Apr 2026 - 11:56

score 225 · Answer 4 · 2026-02-23 06:39:36

225

Views

Find the polynomial of integral coefficient with minimum degree and root $z+z^3+z^9$.

Published on 23 Feb 2026 - 6:39

score 32 · Answer 5 · 2026-03-26 22:53:34

32

Views

A polynomial relation between the lengths of segments that are constructible with straightedge and compass.

Published on 26 Mar 2026 - 22:53

score 420 · Answer 6 · 2026-02-23 06:36:29

420

Views

Given a polynomial with roots $a, b, c, d, e$, find the polynomial whose roots are $abc, abd, abe, ...$

Published on 23 Feb 2026 - 6:36

score 89 · Answer 7 · 2026-03-26 01:09:26

89

Views

Finding solution of $A\mathbf{x} = \mathbf{0}$ from rref over gf(2)

Published on 26 Mar 2026 - 1:09

score 386 · Answer 8 · 2020-04-07 09:33:57

386

Views

If $L/K$ is a field extension, then $L$ is a vector space over $K$

Published on 07 Apr 2020 - 9:33

score 110 · Answer 9 · 2026-03-30 01:48:02

110

Views

Degrees of the irreducible factors of the polynomial $f = X^p-X+a \in \mathbb{F}_q[X]$.

Published on 30 Mar 2026 - 1:48

score 265 · Answer 10 · 2026-03-26 16:07:07

265

Views

Branch points of a dihedral Galois branched cover of a complex torus

Published on 26 Mar 2026 - 16:07

score 182 · Answer 11 · 2026-03-25 08:09:42

182

Views

On the irreducibility over cyclotomic field in radical extension.

Published on 25 Mar 2026 - 8:09

score 295 · Answer 12 · 2026-03-26 07:58:56

295

Views

Quadratic extension $\mathbb{Q}(\sqrt{5})$ inside cyclotomic field $\mathbb{Q}(\zeta_{20})$

Published on 26 Mar 2026 - 7:58

score 48 · Answer 13 · 2026-04-04 12:00:16

48

Views

Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?

Published on 04 Apr 2026 - 12:00

score 198 · Answer 14 · 2026-04-04 13:40:25

198

Views

Is element in infinitely generated field extension contained in finitely generated field extension?

Published on 04 Apr 2026 - 13:40

score 68 · Answer 15 · 2026-03-25 08:09:46

68

Views

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

Published on 25 Mar 2026 - 8:09

List Question

Galois Extensions and Splitting Fields of Separable Polynomials

How to find the minimal basis of an invariant ring?

Condition for Intermediate Field to be Galois

Find the polynomial of integral coefficient with minimum degree and root $z+z^3+z^9$.

A polynomial relation between the lengths of segments that are constructible with straightedge and compass.

Given a polynomial with roots $a, b, c, d, e$, find the polynomial whose roots are $abc, abd, abe, ...$

Finding solution of $A\mathbf{x} = \mathbf{0}$ from rref over gf(2)

If $L/K$ is a field extension, then $L$ is a vector space over $K$

Degrees of the irreducible factors of the polynomial $f = X^p-X+a \in \mathbb{F}_q[X]$.

Branch points of a dihedral Galois branched cover of a complex torus

On the irreducibility over cyclotomic field in radical extension.

Quadratic extension $\mathbb{Q}(\sqrt{5})$ inside cyclotomic field $\mathbb{Q}(\zeta_{20})$

Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?

Is element in infinitely generated field extension contained in finitely generated field extension?

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

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