Question

Let $E/K$ be an algebraic extension. Is $E/(E\cap K^{1/p^\infty})$ necessarily separable?

score 68 · Answer 1 · 2017-03-19 02:22:39

68

Views

Let $E/K$ be an algebraic extension. Is $E/(E\cap K^{1/p^\infty})$ necessarily separable?

Published on 19 Mar 2017 - 2:22

score 182 · Answer 2 · 2026-02-23 01:05:17

182

Views

A finite extension of a normal extension is normal?

Published on 23 Feb 2026 - 1:05

score 1.3k · Answer 3 · 2017-03-19 09:18:10

1.3k

Views

Quadratic extension of field of characteristic 2 can/cannot be obtained by adjoining a single square root

Published on 19 Mar 2017 - 9:18

score 85 · Answer 4 · 2026-03-28 06:59:04

85

Views

Simplification rules for roots of unity

Published on 28 Mar 2026 - 6:59

score 1.1k · Answer 5 · 2017-03-20 16:20:53

1.1k

Views

Subfield of a finitely generated field extension is still finitely generated

Published on 20 Mar 2017 - 16:20

score 48 · Answer 6 · 2017-03-21 06:38:50

48

Views

Is this an example for $[E:\Bbb R]$=4?

Published on 21 Mar 2017 - 6:38

score 51 · Answer 7 · 2017-03-21 17:24:51

51

Views

Determine the minimal polynomial

Published on 21 Mar 2017 - 17:24

score 109 · Answer 8 · 2026-03-25 14:39:52

109

Views

Cyclotomic Extension

Published on 25 Mar 2026 - 14:39

score 59 · Answer 9 · 2017-03-21 19:38:13

Show that $\mathbb{Q}(\sqrt{n},\sqrt{-n})\subseteq\mathbb{Q}(\sqrt{n}+\sqrt{-n})$ by evaluating $\alpha^3+2n\alpha$ and $\alpha^3-2n\alpha$

score 56 · Answer 10 · 2017-03-22 05:46:06

56

Views

Is it possible to have a degree-$1234567890$ extension of $\Bbb Q(\sqrt5)$?

Published on 22 Mar 2017 - 5:46

score 397 · Answer 11 · 2017-03-22 08:22:32

397

Views

Let $K$ be a finite normal extension of a field $F$. Prove that for every $\alpha \in K$, the norm of $\alpha$ over $F$ is in $F$

Published on 22 Mar 2017 - 8:22

score 111 · Answer 12 · 2026-03-25 06:21:21

111

Views

Question regarding fractions of algebraic integers

Published on 25 Mar 2026 - 6:21

score 146 · Answer 13 · 2017-03-22 22:41:16

146

Views

Proof of Field Embedding which does not restrict identity

Published on 22 Mar 2017 - 22:41

score 205 · Answer 14 · 2017-03-23 12:03:28

205

Views

Is the extension $ \mathbb{Q}(\sqrt{2}, \sqrt{3}) $ simple?

Published on 23 Mar 2017 - 12:03

score 120 · Answer 15 · 2017-03-23 12:37:40

120

Views

Relation between field extensions generated by the different roots of a given irreducible polynomial

Published on 23 Mar 2017 - 12:37

List Question

Let $E/K$ be an algebraic extension. Is $E/(E\cap K^{1/p^\infty})$ necessarily separable?

A finite extension of a normal extension is normal?

Quadratic extension of field of characteristic 2 can/cannot be obtained by adjoining a single square root

Simplification rules for roots of unity

Subfield of a finitely generated field extension is still finitely generated

Is this an example for $[E:\Bbb R]$=4?

Determine the minimal polynomial

Cyclotomic Extension

Show that $\mathbb{Q}(\sqrt{n},\sqrt{-n})\subseteq\mathbb{Q}(\sqrt{n}+\sqrt{-n})$ by evaluating $\alpha^3+2n\alpha$ and $\alpha^3-2n\alpha$

Is it possible to have a degree-$1234567890$ extension of $\Bbb Q(\sqrt5)$?

Let $K$ be a finite normal extension of a field $F$. Prove that for every $\alpha \in K$, the norm of $\alpha$ over $F$ is in $F$

Question regarding fractions of algebraic integers

Proof of Field Embedding which does not restrict identity

Is the extension $ \mathbb{Q}(\sqrt{2}, \sqrt{3}) $ simple?

Relation between field extensions generated by the different roots of a given irreducible polynomial

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