Question

Connection between splitting field and quotient ring of polynomials

score 278 · Answer 1 · 2026-04-13 12:26:01

278

Views

Connection between splitting field and quotient ring of polynomials

Published on 13 Apr 2026 - 12:26

score 142 · Answer 2 · 2026-04-15 20:24:25

142

Views

Prove that $\mathbb Q(a + b)$ and $\mathbb Q(a,b)$ are equal under some conditions.

Published on 15 Apr 2026 - 20:24

score 60 · Answer 3 · 2026-04-17 03:49:45

60

Views

Example of an irreducible polynomial $g$ where $(\mathbb{Q}[x]/(g))/\mathbb{Q}$ is not Galois

Published on 17 Apr 2026 - 3:49

score 109 · Answer 4 · 2026-04-15 23:33:08

109

Views

Prove that $\sqrt{\frac{1+\sqrt5}2}$ is not in $\mathbb Q(\sqrt5)$

Published on 15 Apr 2026 - 23:33

score 126 · Answer 5 · 2026-03-27 15:56:16

126

Views

Galois descent of Galois-invariant objects

Published on 27 Mar 2026 - 15:56

score 340 · Answer 6 · 2026-04-15 01:38:58

340

Views

Is the subextension of a purely transcendental extension purely transcendental over the base field?

Published on 15 Apr 2026 - 1:38

score 120 · Answer 7 · 2026-04-14 20:29:59

120

Views

Degree of $\mathbb{Q}(\sqrt[4]{2},i\sqrt[4]{2})$ over $\mathbb Q$

Published on 14 Apr 2026 - 20:29

score 138 · Answer 8 · 2026-04-15 13:46:34

138

Views

Minimal polynomial of $x=\sqrt{2}+i\sqrt{3}$

Published on 15 Apr 2026 - 13:46

score 231 · Answer 9 · 2026-04-16 03:23:40

231

Views

$f\in k[x_1,\ldots,x_n]$ degree $2$ homogeneous polynomial having a non-trivial zero in odd deg extension of $k$ , $f$ has a non-trivial zero in $k$.

Published on 16 Apr 2026 - 3:23

score 119 · Answer 10 · 2026-04-15 18:19:50

119

Views

Group of Square classes of $\mathbb{Q}[i]$

Published on 15 Apr 2026 - 18:19

score 66 · Answer 11 · 2026-04-14 02:23:25

66

Views

Field extension and simplicity

Published on 14 Apr 2026 - 2:23

score 116 · Answer 12 · 2026-03-26 13:01:13

116

Views

Prove that $\{x\}$ is transcendental base of $\mathbb{Q}(x,i)$

Published on 26 Mar 2026 - 13:01

score 37 · Answer 13 · 2026-04-17 04:39:34

37

Views

Separability degree of $\mathbb{Q}(\sqrt{2}, \sqrt[3]{3})/\mathbb{Q}$

Published on 17 Apr 2026 - 4:39

score 177 · Answer 14 · 2026-04-12 01:48:54

177

Views

What is the intuition behind defining this isomorphism?

Published on 12 Apr 2026 - 1:48

score 90 · Answer 15 · 2026-04-17 15:36:46

90

Views

If $F \leq\overline{\mathbb{Q}}(x)$ then either $F/\mathbb{Q}$ or $\overline{\mathbb{Q}}(x)/F$ is algebraic.

Published on 17 Apr 2026 - 15:36

List Question

Connection between splitting field and quotient ring of polynomials

Prove that $\mathbb Q(a + b)$ and $\mathbb Q(a,b)$ are equal under some conditions.

Example of an irreducible polynomial $g$ where $(\mathbb{Q}[x]/(g))/\mathbb{Q}$ is not Galois

Prove that $\sqrt{\frac{1+\sqrt5}2}$ is not in $\mathbb Q(\sqrt5)$

Galois descent of Galois-invariant objects

Is the subextension of a purely transcendental extension purely transcendental over the base field?

Degree of $\mathbb{Q}(\sqrt[4]{2},i\sqrt[4]{2})$ over $\mathbb Q$

Minimal polynomial of $x=\sqrt{2}+i\sqrt{3}$

$f\in k[x_1,\ldots,x_n]$ degree $2$ homogeneous polynomial having a non-trivial zero in odd deg extension of $k$ , $f$ has a non-trivial zero in $k$.

Group of Square classes of $\mathbb{Q}[i]$

Field extension and simplicity

Prove that $\{x\}$ is transcendental base of $\mathbb{Q}(x,i)$

Separability degree of $\mathbb{Q}(\sqrt{2}, \sqrt[3]{3})/\mathbb{Q}$

What is the intuition behind defining this isomorphism?

If $F \leq\overline{\mathbb{Q}}(x)$ then either $F/\mathbb{Q}$ or $\overline{\mathbb{Q}}(x)/F$ is algebraic.

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