Question

The minimal polynomial splits over a field of prime characteristic?

score 28 · Answer 1 · 2024-02-26 00:47:53

28

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The minimal polynomial splits over a field of prime characteristic?

Published on 26 Feb 2024 - 0:47

score 45 · Answer 2 · 2024-03-07 08:02:44

45

Views

Reducing an inseparable polynomial over the same field to a separable polynomial over a field

Published on 07 Mar 2024 - 8:02

score 26 · Answer 3 · 2024-03-07 18:52:38

26

Views

Equivalent definition of a perfect field

Published on 07 Mar 2024 - 18:52

score 33 · Answer 4 · 2024-03-08 10:49:40

33

Views

$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

Published on 08 Mar 2024 - 10:49

score 47 · Answer 5 · 2024-03-11 14:39:13

47

Views

Do we know all non-perfect fields?

Published on 11 Mar 2024 - 14:39

score 42 · Answer 6 · 2024-03-14 11:20:44

42

Views

Showing that any two separable closures of a field are $K$-isomorphic

Published on 14 Mar 2024 - 11:20

score 25 · Answer 7 · 2024-03-21 07:16:46

25

Views

Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Published on 21 Mar 2024 - 7:16

score 32 · Answer 8 · 2024-03-27 16:37:32

32

Views

Equivalence between definitions of purely inseparable extension

Published on 27 Mar 2024 - 16:37

score 22 · Answer 9 · 2024-03-31 05:35:57

22

Views

Proof of a telescoping formula for separable degrees in Hungerford's Algebra.

Published on 31 Mar 2024 - 5:35

score 810 · Answer 10 · 2015-05-23 16:28:40

810

Views

Can a field extension still have "non-separability" above its maximal purely inseparable subextension?

Published on 23 May 2015 - 16:28

score 237 · Answer 11 · 2015-05-24 05:12:09

237

Views

If $F^p = F$ and $E/F$ is algebraic, then $E/F$ is separable and $E^p = E$ : Corollary V.6.12 from Lang's Algebra

Published on 24 May 2015 - 5:12

score 5.3k · Answer 12 · 2013-07-28 23:14:19

5.3k

Views

The definition of the separable closure of a field

Published on 28 Jul 2013 - 23:14

score 114 · Answer 13 · 2026-02-23 02:50:09

114

Views

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

Published on 23 Feb 2026 - 2:50

score 127 · Answer 14 · 2017-05-02 15:17:13

127

Views

$k$ be perfect field , char $p>0$ , $u=f(X)/g(X) \in k(X) ; f(X),g(X) \in k[X]$ relatively prime , $k(X)/k(u)$ separable ; to show $u \notin k(X)^p$

Published on 02 May 2017 - 15:17

score 376 · Answer 15 · 2017-05-04 03:56:16

376

Views

Let $F\subseteq L\subseteq K$ be fields such that $K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal.

Published on 04 May 2017 - 3:56

List Question

The minimal polynomial splits over a field of prime characteristic?

Reducing an inseparable polynomial over the same field to a separable polynomial over a field

Equivalent definition of a perfect field

$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

Do we know all non-perfect fields?

Showing that any two separable closures of a field are $K$-isomorphic

Let $F$ be a field of characteristic $2$. Find the maximal separable subextension in $F(X)/F(X^4 + X^2)$.

Equivalence between definitions of purely inseparable extension

Proof of a telescoping formula for separable degrees in Hungerford's Algebra.

Can a field extension still have "non-separability" above its maximal purely inseparable subextension?

If $F^p = F$ and $E/F$ is algebraic, then $E/F$ is separable and $E^p = E$ : Corollary V.6.12 from Lang's Algebra

The definition of the separable closure of a field

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

$k$ be perfect field , char $p>0$ , $u=f(X)/g(X) \in k(X) ; f(X),g(X) \in k[X]$ relatively prime , $k(X)/k(u)$ separable ; to show $u \notin k(X)^p$

Let $F\subseteq L\subseteq K$ be fields such that $K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal.

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