Question

Are these fields equal?

score 68 · Answer 1 · 2026-04-10 20:27:57

68

Views

Are these fields equal?

Published on 10 Apr 2026 - 20:27

score 49 · Answer 2 · 2026-04-15 07:02:35

49

Views

A family of irreducible solvable polynomials related to numbers of the form $a+b\sqrt{n}$

Published on 15 Apr 2026 - 7:02

score 99 · Answer 3 · 2026-04-15 06:41:03

99

Views

Prove that there is no intermediate field $K$ with $\mathbb{Q}\subset K\subsetneq \mathbb{C}$ with $\mathbb{C}/K$ purely transcendental.

Published on 15 Apr 2026 - 6:41

score 97 · Answer 4 · 2026-04-13 02:49:55

97

Views

Show that the homomorphism from $K[X]$ to $L'$ which takes $X$ to $y$ induces an isomorphism of $L$ with $K(y)$.

Published on 13 Apr 2026 - 2:49

score 73 · Answer 5 · 2026-03-25 22:10:53

73

Views

Find $a, b, c$ such that element $x=a\alpha^2+b\alpha+c \in \mathbb{Q}[x]/\langle x^3+x+11 \rangle$

Published on 25 Mar 2026 - 22:10

score 58 · Answer 6 · 2026-04-15 13:18:44

58

Views

Show that $\frac{1+i}{\sqrt{2}}$ is in the splitting field of $x^8 - 3$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 13:18

score 396 · Answer 7 · 2026-04-12 18:09:01

396

Views

When do the units of a ring together with 0 form a field?

Published on 12 Apr 2026 - 18:09

score 66 · Answer 8 · 2026-04-12 17:05:22

66

Views

Where did we use induction process here?

Published on 12 Apr 2026 - 17:05

score 69 · Answer 9 · 2026-04-14 20:57:39

69

Views

If $ F(a_1, \dots, a_n)$ is splitting field of a separable polynomial $f$, then $[F(a_1, \dots, a_i):F] \leq n(n-1) \cdots (n-i+1)$

Published on 14 Apr 2026 - 20:57

score 120 · Answer 10 · 2026-04-13 09:22:07

120

Views

Splitting Field as Subfield Generated by Roots

Published on 13 Apr 2026 - 9:22

score 49 · Answer 11 · 2026-04-12 11:10:15

49

Views

Little help with some field arithmetic problem

Published on 12 Apr 2026 - 11:10

score 522 · Answer 12 · 2026-04-07 12:14:12

522

Views

$K=\mathbb{Q}(\sqrt[8]{2},i)$ and let $F=\mathbb{Q}(\sqrt{-2})$. Find the Galois Group $G(K,F)$

Published on 07 Apr 2026 - 12:14

score 196 · Answer 13 · 2026-03-25 15:41:08

196

Views

Can the Dedekind completion of the hyperreal numbers be embedded in an ordered field?

Published on 25 Mar 2026 - 15:41

score 66 · Answer 14 · 2026-04-16 11:33:48

66

Views

Show that $\sqrt{2} \notin \mathbb{Q}(a)$ for real numbers a.

Published on 16 Apr 2026 - 11:33

score 316 · Answer 15 · 2026-04-16 02:59:03

316

Views

Let$ K$ be a finite extension of $F$. If $L_1,L_2$ are subfields of $K$ containing $F$ and $L_1⊂ L_2$ then $K$ is simple extension of $F$.

Published on 16 Apr 2026 - 2:59

List Question

Are these fields equal?

A family of irreducible solvable polynomials related to numbers of the form $a+b\sqrt{n}$

Prove that there is no intermediate field $K$ with $\mathbb{Q}\subset K\subsetneq \mathbb{C}$ with $\mathbb{C}/K$ purely transcendental.

Show that the homomorphism from $K[X]$ to $L'$ which takes $X$ to $y$ induces an isomorphism of $L$ with $K(y)$.

Find $a, b, c$ such that element $x=a\alpha^2+b\alpha+c \in \mathbb{Q}[x]/\langle x^3+x+11 \rangle$

Show that $\frac{1+i}{\sqrt{2}}$ is in the splitting field of $x^8 - 3$ over $\mathbb{Q}$

When do the units of a ring together with 0 form a field?

Where did we use induction process here?

If $ F(a_1, \dots, a_n)$ is splitting field of a separable polynomial $f$, then $[F(a_1, \dots, a_i):F] \leq n(n-1) \cdots (n-i+1)$

Splitting Field as Subfield Generated by Roots

Little help with some field arithmetic problem

$K=\mathbb{Q}(\sqrt[8]{2},i)$ and let $F=\mathbb{Q}(\sqrt{-2})$. Find the Galois Group $G(K,F)$

Can the Dedekind completion of the hyperreal numbers be embedded in an ordered field?

Show that $\sqrt{2} \notin \mathbb{Q}(a)$ for real numbers a.

Let$ K$ be a finite extension of $F$. If $L_1,L_2$ are subfields of $K$ containing $F$ and $L_1⊂ L_2$ then $K$ is simple extension of $F$.

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