List questions from extension-field

Published on 15 Apr 2026 - 18:57

52

Views

What algebraic number $k$ satisfy $\mathbb{Q}\left(k,\ i \right) \cong \mathbb{Q}\left(\text{exp} (2\pi i/5)\right)$?

Published on 15 Apr 2026 - 23:37

89

Views

Non-trivial gap in a field extension problem proof

Published on 13 Apr 2026 - 20:40

389

Views

Question about minimal polynomial and extension degree

Published on 12 Apr 2026 - 6:56

81

Views

Proof that if you have two splitting fields for the same polynomial and one of them is contained in a radical extension, then so is the other one.

Published on 15 Apr 2026 - 15:58

225

Views

Quadratic extensions are obtained by adjoining a square root

Published on 12 Apr 2026 - 19:33

35

Views

Does $x^d=x^p$ imply that $d=p$ if $p$ is prime and $2\leq d \leq p$?

Published on 16 Apr 2026 - 11:33

127

Views

For non-constant polynomial $f(x) \in F[x]$ have a zero in $E$ which containing $F$.

Published on 14 Apr 2026 - 21:50

49

Views

$t+1$ transcendent over $K$ if $t$ is transcendent

Published on 26 Mar 2026 - 8:14

22

Views

Question about a four degre extension of $\mathbb{Q}$ Involving polynomials.

Published on 15 Apr 2026 - 18:19

102

Views

Show that $[L : Q(t)]$ is dependent on the choice of inclusion map $\phi$

Published on 14 Apr 2026 - 18:03

127

Views

Finite field extension over a field

Published on 12 Apr 2026 - 2:03

217

Views

Prove that an extension is not simple

Published on 13 Apr 2026 - 9:43

85

Views

Show that the extension has degree 9

Published on 14 Apr 2026 - 7:21

110

Views

Prove that if $\alpha \in E$ and $f(\alpha) = 0$, then $E = E^H(\alpha)$.

Published on 14 Apr 2026 - 14:37

List Question

Prove $\mathbb{Q}(\cos(2\pi/p))\subset \mathbb{Q}(e^{i2\pi/p})$

What algebraic number $k$ satisfy $\mathbb{Q}\left(k,\ i \right) \cong \mathbb{Q}\left(\text{exp} (2\pi i/5)\right)$?

Non-trivial gap in a field extension problem proof

Question about minimal polynomial and extension degree

Proof that if you have two splitting fields for the same polynomial and one of them is contained in a radical extension, then so is the other one.

Quadratic extensions are obtained by adjoining a square root

Does $x^d=x^p$ imply that $d=p$ if $p$ is prime and $2\leq d \leq p$?

For non-constant polynomial $f(x) \in F[x]$ have a zero in $E$ which containing $F$.

$t+1$ transcendent over $K$ if $t$ is transcendent

Question about a four degre extension of $\mathbb{Q}$ Involving polynomials.

Show that $[L : Q(t)]$ is dependent on the choice of inclusion map $\phi$

Finite field extension over a field

Prove that an extension is not simple

Show that the extension has degree 9

Prove that if $\alpha \in E$ and $f(\alpha) = 0$, then $E = E^H(\alpha)$.

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