Question

Isomorphic field extensions have the same degree

score 1.2k · Answer 1 · 2019-02-24 12:30:07

1.2k

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Isomorphic field extensions have the same degree

Published on 24 Feb 2019 - 12:30

score 581 · Answer 2 · 2026-03-27 00:09:43

581

Views

Finding a field extension in which every element has zero trace

Published on 27 Mar 2026 - 0:09

score 272 · Answer 3 · 2019-02-24 21:57:16

272

Views

Indeterminate is Algebraic over Transcendental Extension

Published on 24 Feb 2019 - 21:57

score 149 · Answer 4 · 2019-02-25 11:45:55

149

Views

Why is $\mathbb{Q}(\zeta_7)$ not a radical extension?

Published on 25 Feb 2019 - 11:45

score 16 · Answer 5 · 2026-02-23 02:54:22

16

Views

$L_1L_2/K$ is separable. justify it

Published on 23 Feb 2026 - 2:54

score 47 · Answer 6 · 2019-02-27 03:23:55

47

Views

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

Published on 27 Feb 2019 - 3:23

score 455 · Answer 7 · 2019-02-28 07:10:45

455

Views

$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$

Published on 28 Feb 2019 - 7:10

score 61 · Answer 8 · 2026-03-26 18:51:48

61

Views

Questions about proof of existence of roots of $f$ in $K[X]/(f)$

Published on 26 Mar 2026 - 18:51

score 73 · Answer 9 · 2026-03-28 07:35:07

73

Views

Frobenius morphism associated to field extension

Published on 28 Mar 2026 - 7:35

score 148 · Answer 10 · 2019-03-04 12:46:06

148

Views

Verifying a $K$-basis for a primitive extension $K\subset K(\alpha)$

Published on 04 Mar 2019 - 12:46

score 63 · Answer 11 · 2019-03-04 16:29:06

Let $L/Q$ be a field extension. Let $\sigma\in\textrm{Aut}_Q(L)$. Let $f(x) \in Q[x]$ be a polynomial. Show that $f(σ(α)) = σ(f(α))$ for all $α ∈ L.$

score 134 · Answer 12 · 2019-03-05 18:19:46

134

Views

Showing linear independence of power basis of $\mathbb{Q}(\sqrt[4]{3})$ over $\mathbb{Q}$.

Published on 05 Mar 2019 - 18:19

score 458 · Answer 13 · 2026-03-25 21:01:37

458

Views

Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

Published on 25 Mar 2026 - 21:01

score 69 · Answer 14 · 2019-03-06 17:22:08

69

Views

If $f_{K(\alpha)}^{\beta}\big| f_{K}^{\beta}$, then $\deg\left(f_{K(\alpha)}^{\beta}\right)| \deg\left(f_{K}^{\beta}\right)$?

Published on 06 Mar 2019 - 17:22

score 199 · Answer 15 · 2026-03-25 06:06:17

199

Views

Complete valuation, norm of finite extension. Proof of Propositon.

Published on 25 Mar 2026 - 6:06

List Question

Isomorphic field extensions have the same degree

Finding a field extension in which every element has zero trace

Indeterminate is Algebraic over Transcendental Extension

Why is $\mathbb{Q}(\zeta_7)$ not a radical extension?

$L_1L_2/K$ is separable. justify it

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$

Questions about proof of existence of roots of $f$ in $K[X]/(f)$

Frobenius morphism associated to field extension

Verifying a $K$-basis for a primitive extension $K\subset K(\alpha)$

Let $L/Q$ be a field extension. Let $\sigma\in\textrm{Aut}_Q(L)$. Let $f(x) \in Q[x]$ be a polynomial. Show that $f(σ(α)) = σ(f(α))$ for all $α ∈ L.$

Showing linear independence of power basis of $\mathbb{Q}(\sqrt[4]{3})$ over $\mathbb{Q}$.

Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

If $f_{K(\alpha)}^{\beta}\big| f_{K}^{\beta}$, then $\deg\left(f_{K(\alpha)}^{\beta}\right)| \deg\left(f_{K}^{\beta}\right)$?

Complete valuation, norm of finite extension. Proof of Propositon.

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