Question

Relation between field extensions generated by the different roots of a given irreducible polynomial

score 123 · Answer 1 · 2026-04-15 13:08:31

123

Views

Relation between field extensions generated by the different roots of a given irreducible polynomial

Published on 15 Apr 2026 - 13:08

score 258 · Answer 2 · 2026-04-16 11:17:09

258

Views

Query regarding the use of the KLM theorem for field extensions

Published on 16 Apr 2026 - 11:17

score 547 · Answer 3 · 2026-04-13 04:04:13

547

Views

Embedding of fields

Published on 13 Apr 2026 - 4:04

score 140 · Answer 4 · 2026-04-09 00:56:30

140

Views

Beginner Analysis Question: Are The Field Axioms Any More Than Symbolic Relations

Published on 09 Apr 2026 - 0:56

score 398 · Answer 5 · 2026-05-05 07:41:30

398

Views

$\mathbb{Q}(\sqrt{2}, \sqrt{3})=\mathbb{Q}(\sqrt{2}+\sqrt{3})$

Published on 05 May 2026 - 7:41

score 1.4k · Answer 6 · 2026-04-16 22:12:10

1.4k

Views

Why is $[\mathbb{Q}(\sqrt2,\sqrt3):\mathbb{Q}]=4$?

Published on 16 Apr 2026 - 22:12

score 2.5k · Answer 7 · 2026-04-16 21:07:48

2.5k

Views

$[F(\alpha, \beta): F]=mn$ if $m,n$ are coprime

Published on 16 Apr 2026 - 21:07

score 706 · Answer 8 · 2026-04-15 19:27:15

706

Views

Show that Galois Group $G(K/Q)$ of K over Q is isomorphic to symetric group $S_3$

Published on 15 Apr 2026 - 19:27

score 288 · Answer 9 · 2026-04-16 06:43:24

288

Views

Show that $[K:F]=p^2$ and the separability and inseparability degrees of $K/F$ are both equal to p

Published on 16 Apr 2026 - 6:43

score 252 · Answer 10 · 2026-04-23 14:22:22

252

Views

Explain how to obtain a field with $125$ elements using polynomials by using concrete example provided by a polynomial

Published on 23 Apr 2026 - 14:22

score 804 · Answer 11 · 2026-04-14 22:22:17

804

Views

Examples of extension of $\Bbb Q$ or prove there are no such examples.

Published on 14 Apr 2026 - 22:22

score 327 · Answer 12 · 2026-04-16 17:10:36

327

Views

Define an explicit isomorphism between $\Bbb Q[x]/\langle x^2+1\rangle$ and $\Bbb Q[x]/\langle x^2+4 \rangle$.

Published on 16 Apr 2026 - 17:10

score 681 · Answer 13 · 2026-04-03 05:19:21

681

Views

Prove that the polynomial $x^3+7x+3$ and $x^3+7x+4$ are irreducible over $\Bbb Q.$

Published on 03 Apr 2026 - 5:19

score 194 · Answer 14 · 2026-04-17 07:30:43

194

Views

Are $\Bbb Q[x]/<x^2-1>$ and $\Bbb Q[x]$ isomorphic to any subring of $\Bbb R$?

Published on 17 Apr 2026 - 7:30

score 104 · Answer 15 · 2026-04-14 13:17:31

104

Views

How to formally prove that $\Bbb Q[i]$ is not isomorphic to any subring of $\Bbb R$?

Published on 14 Apr 2026 - 13:17

List Question

Relation between field extensions generated by the different roots of a given irreducible polynomial

Query regarding the use of the KLM theorem for field extensions

Embedding of fields

Beginner Analysis Question: Are The Field Axioms Any More Than Symbolic Relations

$\mathbb{Q}(\sqrt{2}, \sqrt{3})=\mathbb{Q}(\sqrt{2}+\sqrt{3})$

Why is $[\mathbb{Q}(\sqrt2,\sqrt3):\mathbb{Q}]=4$?

$[F(\alpha, \beta): F]=mn$ if $m,n$ are coprime

Show that Galois Group $G(K/Q)$ of K over Q is isomorphic to symetric group $S_3$

Show that $[K:F]=p^2$ and the separability and inseparability degrees of $K/F$ are both equal to p

Explain how to obtain a field with $125$ elements using polynomials by using concrete example provided by a polynomial

Examples of extension of $\Bbb Q$ or prove there are no such examples.

Define an explicit isomorphism between $\Bbb Q[x]/\langle x^2+1\rangle$ and $\Bbb Q[x]/\langle x^2+4 \rangle$.

Prove that the polynomial $x^3+7x+3$ and $x^3+7x+4$ are irreducible over $\Bbb Q.$

Are $\Bbb Q[x]/<x^2-1>$ and $\Bbb Q[x]$ isomorphic to any subring of $\Bbb R$?

How to formally prove that $\Bbb Q[i]$ is not isomorphic to any subring of $\Bbb R$?

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