Question

Find the degree of the extension of $\sqrt{3+2\sqrt{2}}$ over $\mathbb{Q}$.

score 183 · Answer 1 · 2019-07-14 20:52:55

183

Views

Find the degree of the extension of $\sqrt{3+2\sqrt{2}}$ over $\mathbb{Q}$.

Published on 14 Jul 2019 - 20:52

score 61 · Answer 2 · 2026-02-23 03:01:21

61

Views

Let $G$ be a finite group of automorphisms of $E$ and set $F=Fix(G)$, Then why is $E:F$ always separable?

Published on 23 Feb 2026 - 3:01

score 37 · Answer 3 · 2019-07-14 23:27:02

37

Views

Is my line of reasoning correct for considering this fixed field as a simple extension over $GF(7)$?

Published on 14 Jul 2019 - 23:27

score 128 · Answer 4 · 2019-07-18 07:28:29

128

Views

Algebraic independence over subfields and algebraic closure?

Published on 18 Jul 2019 - 7:28

score 31 · Answer 5 · 2026-03-27 07:15:04

31

Views

Under what conditions $[E:F]=\deg(f)$ where $f\in F[x]$ and $E\setminus F$ is a field extension

Published on 27 Mar 2026 - 7:15

score 129 · Answer 6 · 2019-07-18 14:31:58

129

Views

Explicit group decomposition

Published on 18 Jul 2019 - 14:31

score 71 · Answer 7 · 2026-03-28 04:34:54

71

Views

Find a field extension $E/\mathbb{F}_7$ of degree $3$

Published on 28 Mar 2026 - 4:34

score 62 · Answer 8 · 2019-07-18 20:20:53

62

Views

Question about degree of field extension in Galois Theory.

Published on 18 Jul 2019 - 20:20

score 1.3k · Answer 9 · 2026-03-26 02:53:55

1.3k

Views

Proof that every field is perfect?

Published on 26 Mar 2026 - 2:53

score 178 · Answer 10 · 2019-07-19 16:21:31

178

Views

Exercise on the Primitive Element theorem.

Published on 19 Jul 2019 - 16:21

score 545 · Answer 11 · 2026-02-23 02:56:03

545

Views

If $\text{char}(F)\nmid[E:F]$ then $E/F$ is separable

Published on 23 Feb 2026 - 2:56

score 155 · Answer 12 · 2026-03-25 23:58:46

155

Views

How to show that the splitting field of $x^7 - 5$ over $\mathbb{Q}$ is equal to $\mathbb{Q}(\sqrt[7]{5}, \exp(2\pi i/7))$?

Published on 25 Mar 2026 - 23:58

score 99 · Answer 13 · 2019-07-24 01:38:32

99

Views

Purely transcendental extensions do not affect the minimal polynomial.

Published on 24 Jul 2019 - 1:38

score 205 · Answer 14 · 2019-07-25 12:14:15

205

Views

Dummit and Foote 14.4.6

Published on 25 Jul 2019 - 12:14

score 170 · Answer 15 · 2026-03-26 01:26:49

170

Views

Is $\mathbb{Q}(\sqrt3 i) = \mathbb{Q}(\sqrt3, i)$?

Published on 26 Mar 2026 - 1:26

List Question

Find the degree of the extension of $\sqrt{3+2\sqrt{2}}$ over $\mathbb{Q}$.

Let $G$ be a finite group of automorphisms of $E$ and set $F=Fix(G)$, Then why is $E:F$ always separable?

Is my line of reasoning correct for considering this fixed field as a simple extension over $GF(7)$?

Algebraic independence over subfields and algebraic closure?

Under what conditions $[E:F]=\deg(f)$ where $f\in F[x]$ and $E\setminus F$ is a field extension

Explicit group decomposition

Find a field extension $E/\mathbb{F}_7$ of degree $3$

Question about degree of field extension in Galois Theory.

Proof that every field is perfect?

Exercise on the Primitive Element theorem.

If $\text{char}(F)\nmid[E:F]$ then $E/F$ is separable

How to show that the splitting field of $x^7 - 5$ over $\mathbb{Q}$ is equal to $\mathbb{Q}(\sqrt[7]{5}, \exp(2\pi i/7))$?

Purely transcendental extensions do not affect the minimal polynomial.

Dummit and Foote 14.4.6

Is $\mathbb{Q}(\sqrt3 i) = \mathbb{Q}(\sqrt3, i)$?

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