Question

Is every finite extension inside a maximal abelian extension abelian?

score 173 · Answer 1 · 2026-03-25 03:02:27

Is every finite extension inside a maximal abelian extension abelian?

Published on 25 Mar 2026 - 3:02

score 65 · Answer 2 · 2018-06-28 19:39:52

$L/K$ separable extension $[L:K]=3$. $d(L/K)$ discriminant of any basis of $L/K$. $L/K$ Galois if f $d(L/K)$ a square. $\text{char} (K)\neq 2$?

score 432 · Answer 3 · 2026-03-28 16:58:11

432

Views

In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?

Published on 28 Mar 2026 - 16:58

score 389 · Answer 4 · 2018-06-29 05:22:46

389

Views

Arbitrary Ring and Field Contruction

Published on 29 Jun 2018 - 5:22

score 451 · Answer 5 · 2026-03-28 15:21:16

451

Views

Proving the number of K-automorphisms is bounded by the degree of the extension by considering field embeddings

Published on 28 Mar 2026 - 15:21

score 546 · Answer 6 · 2026-03-25 13:05:10

546

Views

Splitting field over a finite field

Published on 25 Mar 2026 - 13:05

score 257 · Answer 7 · 2026-03-24 23:46:14

257

Views

If $n$ divides $m$, prove that $\mathbb{Q}(\zeta_{n}) \subset \mathbb{Q}(\zeta_{m})$

Published on 24 Mar 2026 - 23:46

score 2.5k · Answer 8 · 2018-06-29 22:34:01

2.5k

Views

Show $x^{p^n}-x$ has distinct roots over a field of characteristic $p$.

Published on 29 Jun 2018 - 22:34

score 1.5k · Answer 9 · 2026-03-28 15:25:58

1.5k

Views

$f$ irreducible iff Galois group acts transitively on roots

Published on 28 Mar 2026 - 15:25

score 361 · Answer 10 · 2026-03-25 08:07:39

361

Views

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

Published on 25 Mar 2026 - 8:07

score 339 · Answer 11 · 2026-03-25 12:55:03

339

Views

What are the abelian extensions of $\Bbb C(X)$?

Published on 25 Mar 2026 - 12:55

score 122 · Answer 12 · 2018-06-30 17:11:16

122

Views

Besides using formal derivatives, how can you show that every irreducible polynomial is separable?

Published on 30 Jun 2018 - 17:11

score 116 · Answer 13 · 2018-06-30 23:33:17

116

Views

The idea of field norm

Published on 30 Jun 2018 - 23:33

score 116 · Answer 14 · 2018-07-01 02:26:29

116

Views

Clarification on the definition of irreducible polynomial.

Published on 01 Jul 2018 - 2:26

score 977 · Answer 15 · 2026-03-28 21:06:28

977

Views

The splitting field of $x^4-2$ is $\mathbb{Q}[i+2^{1/4}]$.

Published on 28 Mar 2026 - 21:06

List Question

Is every finite extension inside a maximal abelian extension abelian?

$L/K$ separable extension $[L:K]=3$. $d(L/K)$ discriminant of any basis of $L/K$. $L/K$ Galois if f $d(L/K)$ a square. $\text{char} (K)\neq 2$?

In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?

Arbitrary Ring and Field Contruction

Proving the number of K-automorphisms is bounded by the degree of the extension by considering field embeddings

Splitting field over a finite field

If $n$ divides $m$, prove that $\mathbb{Q}(\zeta_{n}) \subset \mathbb{Q}(\zeta_{m})$

Show $x^{p^n}-x$ has distinct roots over a field of characteristic $p$.

$f$ irreducible iff Galois group acts transitively on roots

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

What are the abelian extensions of $\Bbb C(X)$?

Besides using formal derivatives, how can you show that every irreducible polynomial is separable?

The idea of field norm

Clarification on the definition of irreducible polynomial.

The splitting field of $x^4-2$ is $\mathbb{Q}[i+2^{1/4}]$.

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