Question

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

score 506 · Answer 1 · 2018-05-19 21:58:11

506

Views

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

Published on 19 May 2018 - 21:58

score 656 · Answer 2 · 2026-02-22 21:53:25

656

Views

If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Published on 22 Feb 2026 - 21:53

score 1.1k · Answer 3 · 2018-06-02 14:37:12

1.1k

Views

Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

Published on 02 Jun 2018 - 14:37

score 42 · Answer 4 · 2018-08-02 01:25:43

42

Views

An Upper and Lower Bound for a Field Extension of $\mathbb{Q}$ by a Complex Root

Published on 02 Aug 2018 - 1:25

score 578 · Answer 5 · 2018-08-03 13:16:05

578

Views

A perfect field that is neither of characteristic $0$ nor algebraically closed

Published on 03 Aug 2018 - 13:16

score 559 · Answer 6 · 2018-09-26 12:54:43

559

Views

What is an example of a non-simple finite extension $K/F$ such that the purely inseparable closure of $F$ in $K$ is simple?

Published on 26 Sep 2018 - 12:54

score 152 · Answer 7 · 2018-11-12 21:25:37

152

Views

Show that $\mathbb{Q}[\sqrt{2},\sqrt{3}] $ is separable

Published on 12 Nov 2018 - 21:25

score 38 · Answer 8 · 2018-12-05 12:53:10

38

Views

Problem regarding proving an extension of a field to be separable

Published on 05 Dec 2018 - 12:53

score 59 · Answer 9 · 2019-01-03 16:01:38

59

Views

If $a \in L-k $ satisfies $k(a^n)=L$ (for all $n \geq 1$), then $L/k$ is Galois?

Published on 03 Jan 2019 - 16:01

score 193 · Answer 10 · 2019-01-13 21:47:51

193

Views

Is this a counterexample?

Published on 13 Jan 2019 - 21:47

score 168 · Answer 11 · 2019-01-29 23:46:29

168

Views

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

Published on 29 Jan 2019 - 23:46

score 391 · Answer 12 · 2019-01-30 00:41:13

391

Views

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

Published on 30 Jan 2019 - 0:41

score 305 · Answer 13 · 2019-02-12 11:57:25

305

Views

The multiplicity of a root $r$ of a irreducible polynomial is a power of $p$ characteristic

Published on 12 Feb 2019 - 11:57

score 168 · Answer 14 · 2019-02-16 19:29:10

168

Views

Proof of separability of polynomials without derivatives

Published on 16 Feb 2019 - 19:29

score 194 · Answer 15 · 2019-02-17 10:15:09

194

Views

Lang Steinberg over separably closed field

Published on 17 Feb 2019 - 10:15

List Question

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

An Upper and Lower Bound for a Field Extension of $\mathbb{Q}$ by a Complex Root

A perfect field that is neither of characteristic $0$ nor algebraically closed

What is an example of a non-simple finite extension $K/F$ such that the purely inseparable closure of $F$ in $K$ is simple?

Show that $\mathbb{Q}[\sqrt{2},\sqrt{3}] $ is separable

Problem regarding proving an extension of a field to be separable

If $a \in L-k $ satisfies $k(a^n)=L$ (for all $n \geq 1$), then $L/k$ is Galois?

Is this a counterexample?

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

The multiplicity of a root $r$ of a irreducible polynomial is a power of $p$ characteristic

Proof of separability of polynomials without derivatives

Lang Steinberg over separably closed field

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