Question

Factorize $x^4-4$ in $\mathbb{Q}[x]/(x^4+1)[x]$

score 76 · Answer 1 · 2026-04-17 02:52:05

76

Views

Factorize $x^4-4$ in $\mathbb{Q}[x]/(x^4+1)[x]$

Published on 17 Apr 2026 - 2:52

score 108 · Answer 2 · 2026-04-10 16:58:35

108

Views

degree of field extension / splitting field

Published on 10 Apr 2026 - 16:58

score 68 · Answer 3 · 2026-04-15 07:43:29

68

Views

Finding inverse in a quotient ring

Published on 15 Apr 2026 - 7:43

score 70 · Answer 4 · 2026-04-14 12:12:29

70

Views

Find the Galois group of a quotient field extension

Published on 14 Apr 2026 - 12:12

score 380 · Answer 5 · 2026-04-11 13:06:39

380

Views

Discriminant of a non separable extension

Published on 11 Apr 2026 - 13:06

score 113 · Answer 6 · 2026-04-14 04:06:06

113

Views

How do I find the minimal polynomial of $\sqrt{q}$ with coefficients in $\mathbb{Q}(\sqrt{p})$?

Published on 14 Apr 2026 - 4:06

score 71 · Answer 7 · 2026-04-17 05:23:43

71

Views

Discriminant of odd cyclic Galois extension is not a power of 2

Published on 17 Apr 2026 - 5:23

score 349 · Answer 8 · 2026-04-17 04:28:02

349

Views

Prove factor of $x^3-2$ is irreducible over $\mathbb{Q}(\sqrt[3]{2})$

Published on 17 Apr 2026 - 4:28

score 719 · Answer 9 · 2026-04-13 08:46:48

719

Views

Dimension of generic fiber of a morphism between varieties

Published on 13 Apr 2026 - 8:46

score 78 · Answer 10 · 2026-04-17 11:05:28

78

Views

Find $\gamma$ such that $\mathbb{Q}(\gamma)=\mathbb{Q}(\sqrt{-5},\sqrt{2})$

Published on 17 Apr 2026 - 11:05

score 48 · Answer 11 · 2026-04-17 13:54:16

Find $\gamma$ such that $\mathbb{Q}(\gamma)=\mathbb{Q}(\alpha,\beta)$ where $\alpha$ is a root of $x^3-2x+3$ and $\beta$ is a root of $x^2+x+2$?

score 394 · Answer 12 · 2026-04-11 16:27:09

394

Views

Let E be algebraic extension of F, an embedding maps a root of minimal polynomial to a root of minimal polynomial

Published on 11 Apr 2026 - 16:27

score 42 · Answer 13 · 2026-04-16 02:53:00

42

Views

$G$ is a finite subgroup of $\Gamma(L:K), [L:K] = pq,$ and $[G^{\dagger} : K] > 1,$ prove that $G$ is cyclic.

Published on 16 Apr 2026 - 2:53

score 77 · Answer 14 · 2026-04-16 11:16:52

Let $\alpha$ be algebraic over $F$. Suppose the degree of $\alpha$ over $F$ is odd. Show that $F(\alpha)=F(\alpha^2)$?

score 209 · Answer 15 · 2026-04-09 21:49:42

209

Views

Class of finitely generated extensions is distinguished.

Published on 09 Apr 2026 - 21:49

List Question

Factorize $x^4-4$ in $\mathbb{Q}[x]/(x^4+1)[x]$

degree of field extension / splitting field

Finding inverse in a quotient ring

Find the Galois group of a quotient field extension

Discriminant of a non separable extension

How do I find the minimal polynomial of $\sqrt{q}$ with coefficients in $\mathbb{Q}(\sqrt{p})$?

Discriminant of odd cyclic Galois extension is not a power of 2

Prove factor of $x^3-2$ is irreducible over $\mathbb{Q}(\sqrt[3]{2})$

Dimension of generic fiber of a morphism between varieties

Find $\gamma$ such that $\mathbb{Q}(\gamma)=\mathbb{Q}(\sqrt{-5},\sqrt{2})$

Find $\gamma$ such that $\mathbb{Q}(\gamma)=\mathbb{Q}(\alpha,\beta)$ where $\alpha$ is a root of $x^3-2x+3$ and $\beta$ is a root of $x^2+x+2$?

Let E be algebraic extension of F, an embedding maps a root of minimal polynomial to a root of minimal polynomial

$G$ is a finite subgroup of $\Gamma(L:K), [L:K] = pq,$ and $[G^{\dagger} : K] > 1,$ prove that $G$ is cyclic.

Let $\alpha$ be algebraic over $F$. Suppose the degree of $\alpha$ over $F$ is odd. Show that $F(\alpha)=F(\alpha^2)$?

Class of finitely generated extensions is distinguished.

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