Question

Intermediate fields of degree 6 of $\mathbb{Q}(i,\sqrt{3}, 3^{1/3}):\mathbb{Q}$

score 158 · Answer 1 · 2026-04-17 02:24:06

158

Views

Intermediate fields of degree 6 of $\mathbb{Q}(i,\sqrt{3}, 3^{1/3}):\mathbb{Q}$

Published on 17 Apr 2026 - 2:24

score 70 · Answer 2 · 2026-04-17 10:46:32

70

Views

Having some queries in the proof of $F[x]/Ker(\phi)\simeq F(a)$

Published on 17 Apr 2026 - 10:46

score 736 · Answer 3 · 2026-04-15 04:43:53

736

Views

Is $x^n-a$ irreducible over $\Bbb Q(\zeta_n)$?

Published on 15 Apr 2026 - 4:43

score 365 · Answer 4 · 2026-04-23 06:09:36

365

Views

Necessary and sufﬁcient conditions on m and n for $\Bbb F_{p^n}$ to have a subﬁeld isomorphic with $F_{p^m}$.

Published on 23 Apr 2026 - 6:09

score 32 · Answer 5 · 2026-03-26 18:51:51

32

Views

There is a ring homomorphism of F into E when$|E|$ is not a power of $|F|$

Published on 26 Mar 2026 - 18:51

score 373 · Answer 6 · 2026-03-25 19:51:25

373

Views

Discriminant in char $2$

Published on 25 Mar 2026 - 19:51

score 186 · Answer 7 · 2026-04-15 10:41:03

186

Views

E/F finite extension F'/F any extension. EF' composite field. Prove [EF':F']<=[E:F]

Published on 15 Apr 2026 - 10:41

score 459 · Answer 8 · 2026-04-15 11:29:01

459

Views

Find the splitting field of $x^m-1\in\Bbb F_p$.

Published on 15 Apr 2026 - 11:29

score 545 · Answer 9 · 2026-04-15 22:22:59

545

Views

If $E$ is a splitting field over $F$ for $f,g \in F[x]$, then $f$ is separable over $F$ iff $g$ is separable over $F$.

Published on 15 Apr 2026 - 22:22

score 1.9k · Answer 10 · 2026-04-14 23:59:05

1.9k

Views

Example of a finite extension of a field $F$ that isn't a simple extension of $F$

Published on 14 Apr 2026 - 23:59

score 1.2k · Answer 11 · 2026-04-13 00:20:17

1.2k

Views

Existence and uniquness of a normal closure for an extension field

Published on 13 Apr 2026 - 0:20

score 53 · Answer 12 · 2026-04-14 20:32:27

53

Views

Proving $\dim_K V = \dim_E V \cdot [E:K]$ for a field extension $K \subseteq E$

Published on 14 Apr 2026 - 20:32

score 762 · Answer 13 · 2026-04-23 10:43:30

762

Views

Taking power of element of finite field?

Published on 23 Apr 2026 - 10:43

score 127 · Answer 14 · 2026-04-11 16:11:20

127

Views

What things we have to take care of while finding the degree of field extension, splitting fields for some polynomial?

Published on 11 Apr 2026 - 16:11

score 163 · Answer 15 · 2026-04-13 16:14:14

163

Views

Computing modular inverse in extension fields

Published on 13 Apr 2026 - 16:14

List Question

Intermediate fields of degree 6 of $\mathbb{Q}(i,\sqrt{3}, 3^{1/3}):\mathbb{Q}$

Having some queries in the proof of $F[x]/Ker(\phi)\simeq F(a)$

Is $x^n-a$ irreducible over $\Bbb Q(\zeta_n)$?

Necessary and sufﬁcient conditions on m and n for $\Bbb F_{p^n}$ to have a subﬁeld isomorphic with $F_{p^m}$.

There is a ring homomorphism of F into E when$|E|$ is not a power of $|F|$

Discriminant in char $2$

E/F finite extension F'/F any extension. EF' composite field. Prove [EF':F']<=[E:F]

Find the splitting field of $x^m-1\in\Bbb F_p$.

If $E$ is a splitting field over $F$ for $f,g \in F[x]$, then $f$ is separable over $F$ iff $g$ is separable over $F$.

Example of a finite extension of a field $F$ that isn't a simple extension of $F$

Existence and uniquness of a normal closure for an extension field

Proving $\dim_K V = \dim_E V \cdot [E:K]$ for a field extension $K \subseteq E$

Taking power of element of finite field?

What things we have to take care of while finding the degree of field extension, splitting fields for some polynomial?

Computing modular inverse in extension fields

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