Question

Proving that simple transcendental extensions have infinite degree.

score 300 · Answer 1 · 2026-03-29 08:18:25

300

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Proving that simple transcendental extensions have infinite degree.

Published on 29 Mar 2026 - 8:18

score 192 · Answer 2 · 2026-03-29 23:45:25

192

Views

Any division ring of characteristic $0$ contains a division subring which is isomorphic to $\mathbb{Q}$

Published on 29 Mar 2026 - 23:45

score 126 · Answer 3 · 2026-03-31 23:27:43

126

Views

Primes $p=1\pmod 5$

Published on 31 Mar 2026 - 23:27

score 501 · Answer 4 · 2026-03-25 12:17:21

501

Views

Prove that $\alpha:=\sqrt{\pi}+\sqrt 2 \in \Bbb{C} $ is trancendental over $\Bbb{Q}$.

Published on 25 Mar 2026 - 12:17

score 253 · Answer 5 · 2026-03-25 03:04:20

253

Views

Is the Intertia subgroup the whole Galois group if our finite extension of local fields is totally ramified?

Published on 25 Mar 2026 - 3:04

score 350 · Answer 6 · 2026-03-25 06:21:39

350

Views

Proving there is no smallest positive element of any ordered field F

Published on 25 Mar 2026 - 6:21

score 56 · Answer 7 · 2026-03-25 16:20:46

56

Views

Question on splitting fields.

Published on 25 Mar 2026 - 16:20

score 120 · Answer 8 · 2026-03-25 03:02:58

120

Views

Prove that $2x^4+15x^2+10$ is irreducible in $Q[x]$

Published on 25 Mar 2026 - 3:02

score 136 · Answer 9 · 2026-03-25 16:13:48

136

Views

Splitting field of $f(x) :=x^3+3x^2+3x-4$ over $\Bbb{Q}$ and $\Bbb{Z}_3$.

Published on 25 Mar 2026 - 16:13

score 256 · Answer 10 · 2018-09-11 21:46:10

256

Views

Find the minimal polynomial over $\mathbb{Q}(i)$

Published on 11 Sep 2018 - 21:46

score 228 · Answer 11 · 2018-09-12 14:30:19

228

Views

How to prove that $\mathbb{Q}(\sqrt[3]{2})$ is isomorphic to $\mathbb{Q}(e^{2\pi i/3}\sqrt[3]{2})$

Published on 12 Sep 2018 - 14:30

score 202 · Answer 12 · 2018-09-13 02:27:07

202

Views

Showing the limit points of E are equal to the limit points of E closure.

Published on 13 Sep 2018 - 2:27

score 40 · Answer 13 · 2026-03-25 04:43:03

40

Views

If $b$ is not a prime in $R_1$ then is $R_2$ an integral domain or a field?

Published on 25 Mar 2026 - 4:43

score 117 · Answer 14 · 2026-03-26 02:47:35

117

Views

Given a field $F$ and $R=F[x_1,...x_n]$, show the ideal $(x_1,x_2...x_i)$ is a prime ideal for each i

Published on 26 Mar 2026 - 2:47

score 1.8k · Answer 15 · 2026-03-26 04:53:09

1.8k

Views

Proof that there are exactly $n$ distinct $n$th roots of unity in fields of characteristic zero

Published on 26 Mar 2026 - 4:53

List Question

Proving that simple transcendental extensions have infinite degree.

Any division ring of characteristic $0$ contains a division subring which is isomorphic to $\mathbb{Q}$

Primes $p=1\pmod 5$

Prove that $\alpha:=\sqrt{\pi}+\sqrt 2 \in \Bbb{C} $ is trancendental over $\Bbb{Q}$.

Is the Intertia subgroup the whole Galois group if our finite extension of local fields is totally ramified?

Proving there is no smallest positive element of any ordered field F

Question on splitting fields.

Prove that $2x^4+15x^2+10$ is irreducible in $Q[x]$

Splitting field of $f(x) :=x^3+3x^2+3x-4$ over $\Bbb{Q}$ and $\Bbb{Z}_3$.

Find the minimal polynomial over $\mathbb{Q}(i)$

How to prove that $\mathbb{Q}(\sqrt[3]{2})$ is isomorphic to $\mathbb{Q}(e^{2\pi i/3}\sqrt[3]{2})$

Showing the limit points of E are equal to the limit points of E closure.

If $b$ is not a prime in $R_1$ then is $R_2$ an integral domain or a field?

Given a field $F$ and $R=F[x_1,...x_n]$, show the ideal $(x_1,x_2...x_i)$ is a prime ideal for each i

Proof that there are exactly $n$ distinct $n$th roots of unity in fields of characteristic zero

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