Question

Proving that polynomial f must be of this form if the polynomial is given to be separable

score 402 · Answer 1 · 2021-01-16 15:39:27

402

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Proving that polynomial f must be of this form if the polynomial is given to be separable

Published on 16 Jan 2021 - 15:39

score 269 · Answer 2 · 2021-01-22 08:25:07

269

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A question based on intermediate fields , separable elements , inseparable elements

Published on 22 Jan 2021 - 8:25

score 222 · Answer 3 · 2021-01-22 09:04:28

222

Views

If $\operatorname{char} K =p$ and $[F:K]$ is finite and not divisible by $p$, then $F$ is separable over $K$

Published on 22 Jan 2021 - 9:04

score 134 · Answer 4 · 2021-01-22 11:54:50

134

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How to find degree of separability and degree of inseparability in following question

Published on 22 Jan 2021 - 11:54

score 66 · Answer 5 · 2021-01-29 04:07:21

66

Views

Converse of the result about the composite of purely inseparable extensions

Published on 29 Jan 2021 - 4:07

score 212 · Answer 6 · 2021-02-25 12:48:14

212

Views

What is the intuition behind the definiton of a seperable field extension?

Published on 25 Feb 2021 - 12:48

score 709 · Answer 7 · 2021-03-11 21:22:05

709

Views

prove f is separable if and only if f is relatively prime to its derivative.

Published on 11 Mar 2021 - 21:22

score 165 · Answer 8 · 2021-03-12 10:35:24

165

Views

Why does separable degree behave unexpectedly in infinite extensions?

Published on 12 Mar 2021 - 10:35

score 134 · Answer 9 · 2021-03-21 19:21:44

134

Views

Ring $R'$ with $R\subset R'\subset T$ where $R$, $T$ integrally closed and obtained by a purely inseparable extension

Published on 21 Mar 2021 - 19:21

score 67 · Answer 10 · 2021-04-03 23:50:11

67

Views

Separability degree of extension as number of intermediate separable extensions.

Published on 03 Apr 2021 - 23:50

score 235 · Answer 11 · 2021-04-16 18:23:55

235

Views

Can inseparable elements “appear” in the residue field of the Galois closure of a field extension with separable residue field extension?

Published on 16 Apr 2021 - 18:23

score 60 · Answer 12 · 2021-04-27 23:02:52

60

Views

Properties of $k[x(x-1)]_{\langle x(x-1) \rangle} \subseteq k[x]_{\langle x \rangle}$

Published on 27 Apr 2021 - 23:02

score 117 · Answer 13 · 2021-05-05 10:51:21

117

Views

Base change to algebraic closure commutes with quotient of polynomial ring by maximal ideal

Published on 05 May 2021 - 10:51

score 215 · Answer 14 · 2021-05-05 21:50:57

215

Views

$E$ is the splitting field over $F$ for some separable $f(X) \in F[X]$ implies that $f(X)$ is separable over $\Phi(\Gamma(E/F))$?

Published on 05 May 2021 - 21:50

score 91 · Answer 15 · 2021-05-17 14:10:04

91

Views

$f(x)=x^4+x+1$ is separable over $\Bbb F_p$ iff $p=229$

Published on 17 May 2021 - 14:10

List Question

Proving that polynomial f must be of this form if the polynomial is given to be separable

A question based on intermediate fields , separable elements , inseparable elements

If $\operatorname{char} K =p$ and $[F:K]$ is finite and not divisible by $p$, then $F$ is separable over $K$

How to find degree of separability and degree of inseparability in following question

Converse of the result about the composite of purely inseparable extensions

What is the intuition behind the definiton of a seperable field extension?

prove f is separable if and only if f is relatively prime to its derivative.

Why does separable degree behave unexpectedly in infinite extensions?

Ring $R'$ with $R\subset R'\subset T$ where $R$, $T$ integrally closed and obtained by a purely inseparable extension

Separability degree of extension as number of intermediate separable extensions.

Can inseparable elements “appear” in the residue field of the Galois closure of a field extension with separable residue field extension?

Properties of $k[x(x-1)]_{\langle x(x-1) \rangle} \subseteq k[x]_{\langle x \rangle}$

Base change to algebraic closure commutes with quotient of polynomial ring by maximal ideal

$E$ is the splitting field over $F$ for some separable $f(X) \in F[X]$ implies that $f(X)$ is separable over $\Phi(\Gamma(E/F))$?

$f(x)=x^4+x+1$ is separable over $\Bbb F_p$ iff $p=229$

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