Question

Is there a prime element $\alpha=a+\sqrt{m} b$ such that $N(\alpha)|a$?

score 47 · Answer 1 · 2026-04-15 02:42:44

47

Views

Is there a prime element $\alpha=a+\sqrt{m} b$ such that $N(\alpha)|a$?

Published on 15 Apr 2026 - 2:42

score 71 · Answer 2 · 2026-04-15 09:26:09

71

Views

Confusing question on $\mathbb{Z}_4$ and the polynomial $x^2+x+1$

Published on 15 Apr 2026 - 9:26

score 31 · Answer 3 · 2026-03-26 01:06:12

31

Views

Magma: an algebraic curve having singularities over an unknown extension

Published on 26 Mar 2026 - 1:06

score 55 · Answer 4 · 2026-04-14 20:44:57

55

Views

What is the maximum number of solutions $x\in\mathcal{O}_{\mathbb{Q}[\sqrt{d}]}$ to $x^n=1\mod \alpha\mathcal{O}_{\mathbb{Q}[\sqrt{d}]}$?

Published on 14 Apr 2026 - 20:44

score 43 · Answer 5 · 2026-04-12 19:29:47

43

Views

Finding roots of polynomial over $\mathbb{Q}$ satisfying isomorphism

Published on 12 Apr 2026 - 19:29

score 116 · Answer 6 · 2026-04-13 15:18:35

116

Views

Requesting suggestion for software to solve polynomial equation with coefficients in GF(1024)

Published on 13 Apr 2026 - 15:18

score 59 · Answer 7 · 2026-04-16 22:41:09

59

Views

Prove $\mathbb Q(\sqrt[p]2, \omega_p) = \mathbb Q(\sqrt[p]2+ \omega_p)$.

Published on 16 Apr 2026 - 22:41

score 82 · Answer 8 · 2026-04-15 13:56:07

82

Views

Descent datum on a functor restriction representability criterion

Published on 15 Apr 2026 - 13:56

score 52 · Answer 9 · 2026-04-16 00:02:37

52

Views

Show that there exist $K_0 = \mathbb Q ⊆ K_1 ⊆ K_2 ⊆ K_3 ⊆ K_4 = L$ , where, for $i = 1, . . . , 4$ , $|K_i : K_{i−1}| = 3$.

Published on 16 Apr 2026 - 0:02

score 58 · Answer 10 · 2026-04-14 09:14:02

58

Views

If $c \in \mathbb{Q}(\zeta)$ ,where $\zeta=\zeta_{14}$ is a constructable number ,then $c \in \mathbb{Q}$?

Published on 14 Apr 2026 - 9:14

score 158 · Answer 11 · 2026-03-22 19:56:53

158

Views

$F$ be a field and $F(x)$ be the field of rational functions in $x$ over $F$. Then the element $x$ of $F(x)$ is transcendental over $F$

Published on 22 Mar 2026 - 19:56

score 72 · Answer 12 · 2026-04-17 04:59:48

72

Views

Why is $K((X))$ free module over $K((X^q))$ with basis $1,X,X^2,・・・,X^{q-1}$?

Published on 17 Apr 2026 - 4:59

score 52 · Answer 13 · 2026-04-16 22:26:31

52

Views

$K = Q(\{ \sqrt q : q \text{ is a prime integer}\}) \subset R$. Then $[K : Q]$ is not finite

Published on 16 Apr 2026 - 22:26

score 220 · Answer 14 · 2026-04-17 07:51:49

220

Views

Find $a \in \mathbb C$ such that $\mathbb Q (\zeta_5)= \mathbb Q(\sqrt 5, a)$ and $\left[ \mathbb Q(a): \mathbb Q \right]=2 $.

Published on 17 Apr 2026 - 7:51

score 154 · Answer 15 · 2026-04-12 19:51:09

154

Views

Why weierstrass equation should not be used for elliptic curves over the field char=2?

Published on 12 Apr 2026 - 19:51

List Question

Is there a prime element $\alpha=a+\sqrt{m} b$ such that $N(\alpha)|a$?

Confusing question on $\mathbb{Z}_4$ and the polynomial $x^2+x+1$

Magma: an algebraic curve having singularities over an unknown extension

What is the maximum number of solutions $x\in\mathcal{O}_{\mathbb{Q}[\sqrt{d}]}$ to $x^n=1\mod \alpha\mathcal{O}_{\mathbb{Q}[\sqrt{d}]}$?

Finding roots of polynomial over $\mathbb{Q}$ satisfying isomorphism

Requesting suggestion for software to solve polynomial equation with coefficients in GF(1024)

Prove $\mathbb Q(\sqrt[p]2, \omega_p) = \mathbb Q(\sqrt[p]2+ \omega_p)$.

Descent datum on a functor restriction representability criterion

Show that there exist $K_0 = \mathbb Q ⊆ K_1 ⊆ K_2 ⊆ K_3 ⊆ K_4 = L$ , where, for $i = 1, . . . , 4$ , $|K_i : K_{i−1}| = 3$.

If $c \in \mathbb{Q}(\zeta)$ ,where $\zeta=\zeta_{14}$ is a constructable number ,then $c \in \mathbb{Q}$?

$F$ be a field and $F(x)$ be the field of rational functions in $x$ over $F$. Then the element $x$ of $F(x)$ is transcendental over $F$

Why is $K((X))$ free module over $K((X^q))$ with basis $1,X,X^2,・・・,X^{q-1}$?

$K = Q(\{ \sqrt q : q \text{ is a prime integer}\}) \subset R$. Then $[K : Q]$ is not finite

Find $a \in \mathbb C$ such that $\mathbb Q (\zeta_5)= \mathbb Q(\sqrt 5, a)$ and $\left[ \mathbb Q(a): \mathbb Q \right]=2 $.

Why weierstrass equation should not be used for elliptic curves over the field char=2?

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