Question

Galois Group of $\mathbb Q(\zeta_{np}) / \mathbb Q(\zeta_{n/p})$ is cyclic for a prime $p\mid n$.

score 183 · Answer 1 · 2026-04-16 06:25:45

183

Views

Galois Group of $\mathbb Q(\zeta_{np}) / \mathbb Q(\zeta_{n/p})$ is cyclic for a prime $p\mid n$.

Published on 16 Apr 2026 - 6:25

score 118 · Answer 2 · 2026-04-09 09:12:06

118

Views

Definition of Algebraically Independent Numbers

Published on 09 Apr 2026 - 9:12

score 249 · Answer 3 · 2026-04-10 22:42:18

249

Views

does there exist a transcendental extension of $\mathbb{C}$

Published on 10 Apr 2026 - 22:42

score 129 · Answer 4 · 2026-04-15 16:26:19

129

Views

Basis of the field $E$=$\mathbb{Q}(\sqrt{6}i-\sqrt{5})$.

Published on 15 Apr 2026 - 16:26

score 35 · Answer 5 · 2026-04-11 23:19:31

35

Views

Finding an extension field

Published on 11 Apr 2026 - 23:19

score 53 · Answer 6 · 2026-04-10 15:06:34

53

Views

A problem on extension field

Published on 10 Apr 2026 - 15:06

score 63 · Answer 7 · 2026-04-12 06:57:14

63

Views

When does a dominant morphism of varieties induce a free extension of coordinate algebras?

Published on 12 Apr 2026 - 6:57

score 93 · Answer 8 · 2026-04-15 18:40:25

93

Views

example of a simple Galois extension over $\mathbb{Q}$

Published on 15 Apr 2026 - 18:40

score 33 · Answer 9 · 2026-04-17 00:19:50

33

Views

$\mathbb{F}_pG/J(\mathbb{F}_pG)$ is a separable $\mathbb{F}_p$-algebra

Published on 17 Apr 2026 - 0:19

score 32 · Answer 10 · 2026-04-13 19:05:47

32

Views

independency of power of linear independent elements in a field extension

Published on 13 Apr 2026 - 19:05

score 115 · Answer 11 · 2026-04-10 15:21:16

115

Views

Relationship between ideals in an algebra to ideals after extending scalars

Published on 10 Apr 2026 - 15:21

score 80 · Answer 12 · 2026-04-16 21:50:22

80

Views

$\mathbb{Q}(\sqrt{2},\sqrt{3})$ is isomorphic to $\mathbb{Q}[x]/((x^2-2)(x^2-3))$?

Published on 16 Apr 2026 - 21:50

score 102 · Answer 13 · 2026-04-17 12:39:48

102

Views

Verify that $\mathbb{Q}[\sqrt[3]2]=\{a+b\sqrt[3]2+c\sqrt[3]2^2\,\mid\, a,b,c \in \mathbb{Q}\}$ is a subfield of $\mathbb{R}$

Published on 17 Apr 2026 - 12:39

score 359 · Answer 14 · 2026-04-14 11:46:58

359

Views

If a real number can be expressed in terms of complex solutions of cubic equations, can it be expressed in terms of real solutions of cubic equations?

Published on 14 Apr 2026 - 11:46

score 39 · Answer 15 · 2026-04-12 07:59:41

39

Views

Irreducibility of a polynomial given a condition on the sum of its roots

Published on 12 Apr 2026 - 7:59

List Question

Galois Group of $\mathbb Q(\zeta_{np}) / \mathbb Q(\zeta_{n/p})$ is cyclic for a prime $p\mid n$.

Definition of Algebraically Independent Numbers

does there exist a transcendental extension of $\mathbb{C}$

Basis of the field $E$=$\mathbb{Q}(\sqrt{6}i-\sqrt{5})$.

Finding an extension field

A problem on extension field

When does a dominant morphism of varieties induce a free extension of coordinate algebras?

example of a simple Galois extension over $\mathbb{Q}$

$\mathbb{F}_pG/J(\mathbb{F}_pG)$ is a separable $\mathbb{F}_p$-algebra

independency of power of linear independent elements in a field extension

Relationship between ideals in an algebra to ideals after extending scalars

$\mathbb{Q}(\sqrt{2},\sqrt{3})$ is isomorphic to $\mathbb{Q}[x]/((x^2-2)(x^2-3))$?

Verify that $\mathbb{Q}[\sqrt[3]2]=\{a+b\sqrt[3]2+c\sqrt[3]2^2\,\mid\, a,b,c \in \mathbb{Q}\}$ is a subfield of $\mathbb{R}$

If a real number can be expressed in terms of complex solutions of cubic equations, can it be expressed in terms of real solutions of cubic equations?

Irreducibility of a polynomial given a condition on the sum of its roots

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