Question

Subset Field and Irrdeduciblity

score 27 · Answer 1 · 2026-04-06 00:14:25

27

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Subset Field and Irrdeduciblity

Published on 06 Apr 2026 - 0:14

score 992 · Answer 2 · 2015-11-02 22:02:36

992

Views

Find the Irreducible Polynomial of This Element over $\mathbb Q$

Published on 02 Nov 2015 - 22:02

score 178 · Answer 3 · 2015-11-03 05:01:46

178

Views

Is it true that $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$?

Published on 03 Nov 2015 - 5:01

score 33 · Answer 4 · 2015-11-07 15:55:28

33

Views

Shows that some surds cannot satisfy this equation

Published on 07 Nov 2015 - 15:55

score 2.6k · Answer 5 · 2015-11-07 18:58:25

2.6k

Views

Does every infinite field contain a countably infinite subfield?

Published on 07 Nov 2015 - 18:58

score 706 · Answer 6 · 2026-04-03 10:38:33

706

Views

Without the Axiom of Choice, does every infinite field contain a countably infinite subfield?

Published on 03 Apr 2026 - 10:38

score 430 · Answer 7 · 2026-04-07 19:00:50

430

Views

Proof Verification Regarding Image of $K$-homomorphisms of a Normal Extension

Published on 07 Apr 2026 - 19:00

score 189 · Answer 8 · 2015-11-09 21:53:33

189

Views

Extension field over the field of rational numbers

Published on 09 Nov 2015 - 21:53

score 221 · Answer 9 · 2015-11-11 04:08:55

221

Views

Find a primitive element for the extension $Q(3^{1/4}, i)/Q$

Published on 11 Nov 2015 - 4:08

score 272 · Answer 10 · 2015-11-12 20:35:44

272

Views

Linear independence over an extension

Published on 12 Nov 2015 - 20:35

score 29 · Answer 11 · 2015-11-13 15:18:08

29

Views

find the relation $\beta = f(\alpha)$ when $\beta \in Q(\alpha)$

Published on 13 Nov 2015 - 15:18

score 63 · Answer 12 · 2026-04-09 03:28:19

63

Views

Maximal proper subfields and the behavior of the norm

Published on 09 Apr 2026 - 3:28

score 133 · Answer 13 · 2015-11-15 12:53:04

133

Views

Determining Invariant Elements under a Subgroup of the Galois Group

Published on 15 Nov 2015 - 12:53

score 868 · Answer 14 · 2015-11-16 08:51:42

868

Views

Normal extension, why $\mathbb Q(\sqrt[3]2)/\mathbb Q$ is not normal and $\mathbb Q(\sqrt[3]2,\zeta_3)/\mathbb Q$ is normal.

Published on 16 Nov 2015 - 8:51

score 40 · Answer 15 · 2015-11-16 11:30:23

40

Views

If $K\subset F_i\subset L$, $i=1,2$ are two normal extension of $K$, show that $F_1\cap F_2$ is normal on $K$.

Published on 16 Nov 2015 - 11:30

List Question

Subset Field and Irrdeduciblity

Find the Irreducible Polynomial of This Element over $\mathbb Q$

Is it true that $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$?

Shows that some surds cannot satisfy this equation

Does every infinite field contain a countably infinite subfield?

Without the Axiom of Choice, does every infinite field contain a countably infinite subfield?

Proof Verification Regarding Image of $K$-homomorphisms of a Normal Extension

Extension field over the field of rational numbers

Find a primitive element for the extension $Q(3^{1/4}, i)/Q$

Linear independence over an extension

find the relation $\beta = f(\alpha)$ when $\beta \in Q(\alpha)$

Maximal proper subfields and the behavior of the norm

Determining Invariant Elements under a Subgroup of the Galois Group

Normal extension, why $\mathbb Q(\sqrt[3]2)/\mathbb Q$ is not normal and $\mathbb Q(\sqrt[3]2,\zeta_3)/\mathbb Q$ is normal.

If $K\subset F_i\subset L$, $i=1,2$ are two normal extension of $K$, show that $F_1\cap F_2$ is normal on $K$.

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