Question

Construct the Galois closure of $\mathbb{Q} \subset \mathbb{Q}(\sqrt[4]2)$.

score 507 · Answer 1 · 2019-10-05 15:49:04

507

Views

Construct the Galois closure of $\mathbb{Q} \subset \mathbb{Q}(\sqrt[4]2)$.

Published on 05 Oct 2019 - 15:49

score 124 · Answer 2 · 2019-10-06 00:46:10

124

Views

Extension field with roots of unity(Basis and generator of the field As the vector space)

Published on 06 Oct 2019 - 0:46

score 103 · Answer 3 · 2026-03-30 17:02:45

103

Views

Galois theory and schemes (Mumford & Oda)

Published on 30 Mar 2026 - 17:02

score 80 · Answer 4 · 2019-10-07 12:47:53

80

Views

Ring of invariants of $R \otimes_k \bar{k}$ under Galois action

Published on 07 Oct 2019 - 12:47

score 52 · Answer 5 · 2019-10-07 14:35:35

52

Views

Find the $A_3$-invariant field of $K$

Published on 07 Oct 2019 - 14:35

score 142 · Answer 6 · 2026-03-30 23:47:49

142

Views

Solving a six-degree polynomial of the form $ax^6+bx^3+g$.

Published on 30 Mar 2026 - 23:47

score 1.4k · Answer 7 · 2026-03-29 07:00:24

1.4k

Views

Prove that any polynomial $f(x)\in K[X]$, where $K$ is a field, can be uniquely factored into a product of irreducible polynomials times a constant.

Published on 29 Mar 2026 - 7:00

score 593 · Answer 8 · 2026-04-03 06:55:02

593

Views

About the Galois group of the polynomial $f(x)=x^4+ax^2+b$ over $\mathbb Q$

Published on 03 Apr 2026 - 6:55

score 211 · Answer 9 · 2026-03-30 10:15:28

211

Views

Reference request for introductory Field Theory.

Published on 30 Mar 2026 - 10:15

score 81 · Answer 10 · 2026-04-03 05:28:58

81

Views

Prove that a certain ideal $I$ of $\mathbb Z [x]$ is not a principal ideal.

Published on 03 Apr 2026 - 5:28

score 78 · Answer 11 · 2026-03-28 06:13:20

78

Views

Express the other roots with the powers of $\alpha$.

Published on 28 Mar 2026 - 6:13

score 278 · Answer 12 · 2026-04-01 19:04:00

278

Views

Galois group of quartic polynomial

Published on 01 Apr 2026 - 19:04

score 169 · Answer 13 · 2019-10-12 16:10:19

169

Views

Intersection of Decomposition groups

Published on 12 Oct 2019 - 16:10

score 68 · Answer 14 · 2019-10-12 16:18:48

68

Views

$\operatorname{Gal}(k(t^{1/p},u^{1/p}) / k(t, u))$ contains only identity automorphism.

Published on 12 Oct 2019 - 16:18

score 90 · Answer 15 · 2026-04-03 06:53:34

90

Views

Must a field extension contain an element of particular degree?

Published on 03 Apr 2026 - 6:53

List Question

Construct the Galois closure of $\mathbb{Q} \subset \mathbb{Q}(\sqrt[4]2)$.

Extension field with roots of unity(Basis and generator of the field As the vector space)

Galois theory and schemes (Mumford & Oda)

Ring of invariants of $R \otimes_k \bar{k}$ under Galois action

Find the $A_3$-invariant field of $K$

Solving a six-degree polynomial of the form $ax^6+bx^3+g$.

Prove that any polynomial $f(x)\in K[X]$, where $K$ is a field, can be uniquely factored into a product of irreducible polynomials times a constant.

About the Galois group of the polynomial $f(x)=x^4+ax^2+b$ over $\mathbb Q$

Reference request for introductory Field Theory.

Prove that a certain ideal $I$ of $\mathbb Z [x]$ is not a principal ideal.

Express the other roots with the powers of $\alpha$.

Galois group of quartic polynomial

Intersection of Decomposition groups

$\operatorname{Gal}(k(t^{1/p},u^{1/p}) / k(t, u))$ contains only identity automorphism.

Must a field extension contain an element of particular degree?

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