Question

Basis for the field extension $\mathbb{Q}(3^{1/4},i)$ over $\mathbb{Q}$

score 1.5k · Answer 1 · 2026-03-25 13:54:48

1.5k

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Basis for the field extension $\mathbb{Q}(3^{1/4},i)$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 13:54

score 91 · Answer 2 · 2026-03-25 13:58:09

91

Views

Let $K$ be an extension of $F$. When is $ \operatorname{Aut}(K)= \operatorname{Gal}(K/F)$?

Published on 25 Mar 2026 - 13:58

score 58 · Answer 3 · 2018-04-17 21:30:42

58

Views

Basic question on quadratic fields

Published on 17 Apr 2018 - 21:30

score 882 · Answer 4 · 2026-03-25 15:52:41

882

Views

Clarification of: $f$ has no multiple root in any field extension of $F$ unless $f'$ is the zero polynomial

Published on 25 Mar 2026 - 15:52

score 156 · Answer 5 · 2026-03-25 04:42:53

156

Views

Tensor troubles: Finding product of fields isomorphic to a given tensor product of field extensions of $\mathbb{Q}$

Published on 25 Mar 2026 - 4:42

score 611 · Answer 6 · 2026-03-25 15:53:04

611

Views

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Published on 25 Mar 2026 - 15:53

score 219 · Answer 7 · 2018-04-18 17:36:19

219

Views

Do there exist two non-isomorphic fields whose additive groups are isomorphic and whose multiplicative groups are isomorphic

Published on 18 Apr 2018 - 17:36

score 457 · Answer 8 · 2018-04-18 20:32:23

457

Views

Possible proof of $f(1) = 1$ if $f$ is homomorphism between fields

Published on 18 Apr 2018 - 20:32

score 62 · Answer 9 · 2026-03-22 23:47:56

62

Views

Intermediate Fields and Root Fields

Published on 22 Mar 2026 - 23:47

score 60 · Answer 10 · 2026-03-25 15:54:40

60

Views

How can I show $\sqrt{2-\sqrt{2}} \in \mathbb Q\Big(\sqrt{2+\sqrt{2}}\Big)$?

Published on 25 Mar 2026 - 15:54

score 217 · Answer 11 · 2026-03-25 11:54:18

217

Views

What is meant by 'scalars in modules'?

Published on 25 Mar 2026 - 11:54

score 189 · Answer 12 · 2026-03-24 17:30:11

189

Views

Adjoining square root of a discriminant

Published on 24 Mar 2026 - 17:30

score 74 · Answer 13 · 2026-03-26 01:28:11

74

Views

Showing a finite field isomorphism

Published on 26 Mar 2026 - 1:28

score 37 · Answer 14 · 2026-03-25 11:04:54

37

Views

Fields with the property $\Bbb{F}^\times / \{1, -1\}$ is isomorphic to a subgroup of $\Bbb{F}^\times$.

Published on 25 Mar 2026 - 11:04

score 367 · Answer 15 · 2026-03-25 04:25:16

367

Views

Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.

Published on 25 Mar 2026 - 4:25

List Question

Basis for the field extension $\mathbb{Q}(3^{1/4},i)$ over $\mathbb{Q}$

Let $K$ be an extension of $F$. When is $ \operatorname{Aut}(K)= \operatorname{Gal}(K/F)$?

Basic question on quadratic fields

Clarification of: $f$ has no multiple root in any field extension of $F$ unless $f'$ is the zero polynomial

Tensor troubles: Finding product of fields isomorphic to a given tensor product of field extensions of $\mathbb{Q}$

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Do there exist two non-isomorphic fields whose additive groups are isomorphic and whose multiplicative groups are isomorphic

Possible proof of $f(1) = 1$ if $f$ is homomorphism between fields

Intermediate Fields and Root Fields

How can I show $\sqrt{2-\sqrt{2}} \in \mathbb Q\Big(\sqrt{2+\sqrt{2}}\Big)$?

What is meant by 'scalars in modules'?

Adjoining square root of a discriminant

Showing a finite field isomorphism

Fields with the property $\Bbb{F}^\times / \{1, -1\}$ is isomorphic to a subgroup of $\Bbb{F}^\times$.

Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.

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