List questions from extension-field

144

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Let $F = F_0(t_1^p, t_2^p)$ and $L = F_0(t_1, t_2)$. Show that if $\theta \in L - F$ then $[F(\theta) : F] = p$

Published on 18 May 2018 - 6:44

400

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Minimal polynomial of $\alpha+i$ over $\mathbb{Q}$

Published on 19 May 2018 - 22:35

337

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Basis of the integer ring of $\mathbb{Q}(\sqrt5)$

Published on 23 Mar 2026 - 9:32

47

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Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

Published on 25 Mar 2026 - 9:50

137

Views

Help finding the minimal polynomial of $\beta$ over $GF(19)$

Published on 21 May 2018 - 0:09

69

Views

Verification of Computation of Galois group

Published on 25 Mar 2026 - 11:33

251

Views

Is there a general method to find the size of the Galois group of a cubic polynomial over $\mathbb{Q}$?

Published on 21 May 2018 - 3:38

64

Views

If a rational function satisfies $h(t)=h(1/t)$, then $h(t)=f(t+1/t)$

Published on 25 Mar 2026 - 11:07

59

Views

Group Isomorphism unique element representation

Published on 23 Mar 2026 - 3:53

108

Views

Splitting field over field extenstion

Published on 25 Mar 2026 - 13:04

991

Views

Prove $\mathbb{Q}(2^{1/4})/ \mathbb{Q}$ is NOT a Galois extension.

Published on 22 May 2018 - 20:14

77

Views

Finding all $F $ automorphisms

Published on 23 May 2018 - 5:04

94

Views

If $\text{char}(k)=p$, $K=k(x,y), F=k(x^p,y^p)$, then $[K:F]=P^2$

Published on 23 May 2018 - 7:26

72

Views

Can we view a vector space as a field extention?

Published on 23 May 2018 - 10:15

69

Views

How can $p^f-p^{f-1}$ divide 2?

Published on 23 May 2018 - 17:38

List Question

Let $F = F_0(t_1^p, t_2^p)$ and $L = F_0(t_1, t_2)$. Show that if $\theta \in L - F$ then $[F(\theta) : F] = p$

Minimal polynomial of $\alpha+i$ over $\mathbb{Q}$

Basis of the integer ring of $\mathbb{Q}(\sqrt5)$

Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

Help finding the minimal polynomial of $\beta$ over $GF(19)$

Verification of Computation of Galois group

Is there a general method to find the size of the Galois group of a cubic polynomial over $\mathbb{Q}$?

If a rational function satisfies $h(t)=h(1/t)$, then $h(t)=f(t+1/t)$

Group Isomorphism unique element representation

Splitting field over field extenstion

Prove $\mathbb{Q}(2^{1/4})/ \mathbb{Q}$ is NOT a Galois extension.

Finding all $F $ automorphisms

If $\text{char}(k)=p$, $K=k(x,y), F=k(x^p,y^p)$, then $[K:F]=P^2$

Can we view a vector space as a field extention?

How can $p^f-p^{f-1}$ divide 2?

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