Question

Is $\sqrt{2+\sqrt{2}}+\sqrt[3]{3}/2$ an algebraic integer?

score 88 · Answer 1 · 2026-04-15 18:10:04

88

Views

Is $\sqrt{2+\sqrt{2}}+\sqrt[3]{3}/2$ an algebraic integer?

Published on 15 Apr 2026 - 18:10

score 96 · Answer 2 · 2026-04-12 20:11:14

96

Views

Is the composite of splitting field and random field also Galois over base field?

Published on 12 Apr 2026 - 20:11

score 27 · Answer 3 · 2026-04-14 01:45:02

27

Views

Constraints on $z$ such that $z r_1, \ldots, z r_n$ still have the same minimal polymial

Published on 14 Apr 2026 - 1:45

score 95 · Answer 4 · 2026-04-12 13:25:28

95

Views

Radicals ideals equal in field extension

Published on 12 Apr 2026 - 13:25

score 133 · Answer 5 · 2026-04-16 21:17:43

133

Views

For what $c \in \mathbb{Q}$ is $\sqrt{2}+c\sqrt{3}$ a primitive element of $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

Published on 16 Apr 2026 - 21:17

score 40 · Answer 6 · 2026-04-14 01:34:51

40

Views

What does it mean to find minimal polynomial of $\beta$ over some $F[\alpha]$?

Published on 14 Apr 2026 - 1:34

score 86 · Answer 7 · 2026-04-16 23:05:38

86

Views

Algebraic numbers with special properties

Published on 16 Apr 2026 - 23:05

score 327 · Answer 8 · 2026-04-15 19:01:52

327

Views

Third root of unity $\zeta$, extension degree of $\mathbb{Q}(\sqrt{2},\zeta)$, its $\mathbb{Q}$-Basis and extension of field morphism.

Published on 15 Apr 2026 - 19:01

score 55 · Answer 9 · 2026-04-17 06:15:27

55

Views

Dimension of splitting field of $(x^3+x+1)(x^2+1) \in \mathbb{Q}[x]$ over $\mathbb{Q}$

Published on 17 Apr 2026 - 6:15

score 106 · Answer 10 · 2026-04-15 14:43:40

106

Views

$F$ is a field such that for every $a\in F, a^4=a$, then what is the characteristic of $F$?

Published on 15 Apr 2026 - 14:43

score 214 · Answer 11 · 2026-04-13 11:07:03

214

Views

Confusion about roots of unity over a field of characteristic $p$

Published on 13 Apr 2026 - 11:07

score 176 · Answer 12 · 2026-04-14 14:09:47

176

Views

Determining the degrees of the irreducible factors of $X^{19}-1$

Published on 14 Apr 2026 - 14:09

score 104 · Answer 13 · 2026-04-17 01:35:36

104

Views

Finding ${\rm Aut}_{\mathbb{F}_{27}}(\mathbb{F}_{19683})$

Published on 17 Apr 2026 - 1:35

score 47 · Answer 14 · 2026-04-15 20:59:54

$\Sigma_i a_ib_i = 0$ implies $\Sigma_i \sigma_1(a_i)\sigma_2(b_i) = 0$ for $\sigma_i\in\mathrm{Aut}(F_i),i=1,2$ that agree in $F_1\cap F_2$?

score 47 · Answer 15 · 2026-04-14 00:42:26

47

Views

Question on algebraic integers.

Published on 14 Apr 2026 - 0:42

List Question

Is $\sqrt{2+\sqrt{2}}+\sqrt[3]{3}/2$ an algebraic integer?

Is the composite of splitting field and random field also Galois over base field?

Constraints on $z$ such that $z r_1, \ldots, z r_n$ still have the same minimal polymial

Radicals ideals equal in field extension

For what $c \in \mathbb{Q}$ is $\sqrt{2}+c\sqrt{3}$ a primitive element of $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

What does it mean to find minimal polynomial of $\beta$ over some $F[\alpha]$?

Algebraic numbers with special properties

Third root of unity $\zeta$, extension degree of $\mathbb{Q}(\sqrt{2},\zeta)$, its $\mathbb{Q}$-Basis and extension of field morphism.

Dimension of splitting field of $(x^3+x+1)(x^2+1) \in \mathbb{Q}[x]$ over $\mathbb{Q}$

$F$ is a field such that for every $a\in F, a^4=a$, then what is the characteristic of $F$?

Confusion about roots of unity over a field of characteristic $p$

Determining the degrees of the irreducible factors of $X^{19}-1$

Finding ${\rm Aut}_{\mathbb{F}_{27}}(\mathbb{F}_{19683})$

$\Sigma_i a_ib_i = 0$ implies $\Sigma_i \sigma_1(a_i)\sigma_2(b_i) = 0$ for $\sigma_i\in\mathrm{Aut}(F_i),i=1,2$ that agree in $F_1\cap F_2$?

Question on algebraic integers.

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