Question

Query regarding the use of the KLM theorem for field extensions

score 255 · Answer 1 · 2017-03-23 17:18:18

255

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Query regarding the use of the KLM theorem for field extensions

Published on 23 Mar 2017 - 17:18

score 290 · Answer 2 · 2017-03-23 17:59:38

290

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field of fractions of finite ring extension

Published on 23 Mar 2017 - 17:59

score 1.4k · Answer 3 · 2017-03-24 03:08:44

1.4k

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

Published on 24 Mar 2017 - 3:08

score 2.5k · Answer 4 · 2017-03-24 07:29:30

2.5k

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

Published on 24 Mar 2017 - 7:29

score 285 · Answer 5 · 2017-03-24 19:11:05

285

Views

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

Published on 24 Mar 2017 - 19:11

score 802 · Answer 6 · 2026-04-03 03:36:21

802

Views

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

Published on 03 Apr 2026 - 3:36

score 324 · Answer 7 · 2017-03-25 11:07:32

324

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 25 Mar 2017 - 11:07

score 681 · Answer 8 · 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 191 · Answer 9 · 2017-03-25 14:35:30

191

Views

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

Published on 25 Mar 2017 - 14:35

score 101 · Answer 10 · 2017-03-25 15:26:19

101

Views

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

Published on 25 Mar 2017 - 15:26

score 300 · Answer 11 · 2026-04-03 05:19:21

300

Views

How to determine $[\Bbb Q(\sqrt2,\sqrt{-3}):\Bbb Q]$ and $[\Bbb Q(\sqrt[3]2,\zeta_3\sqrt[3]{2}):\Bbb Q]$?

Published on 03 Apr 2026 - 5:19

score 889 · Answer 12 · 2026-03-27 09:48:11

889

Views

Why the element $t \in F(t)$ is transcendental over $F$?

Published on 27 Mar 2026 - 9:48

score 349 · Answer 13 · 2017-03-26 01:05:23

349

Views

Galois Group of any polynomial over $\mathbb{R}$

Published on 26 Mar 2017 - 1:05

score 1.1k · Answer 14 · 2026-04-03 05:21:05

1.1k

Views

How to prove that the polynomial $x^3-5$ is irreducible over $\Bbb Q(\sqrt2)$?

Published on 03 Apr 2026 - 5:21

score 684 · Answer 15 · 2026-04-03 05:18:01

684

Views

Find the minimal polynomial of $\alpha^2+1$ over $\Bbb F_2$

Published on 03 Apr 2026 - 5:18

List Question

Query regarding the use of the KLM theorem for field extensions

field of fractions of finite ring extension

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

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

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

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 $\Bbb R$?

How to determine $[\Bbb Q(\sqrt2,\sqrt{-3}):\Bbb Q]$ and $[\Bbb Q(\sqrt[3]2,\zeta_3\sqrt[3]{2}):\Bbb Q]$?

Why the element $t \in F(t)$ is transcendental over $F$?

Galois Group of any polynomial over $\mathbb{R}$

How to prove that the polynomial $x^3-5$ is irreducible over $\Bbb Q(\sqrt2)$?

Find the minimal polynomial of $\alpha^2+1$ over $\Bbb F_2$

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