Question

Extension of Splitting Fields over An Arbitrary Field

score 111 · Answer 1 · 2026-03-25 23:56:34

111

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Extension of Splitting Fields over An Arbitrary Field

Published on 25 Mar 2026 - 23:56

score 791 · Answer 2 · 2026-03-25 06:24:56

791

Views

Group automorphism of multiplicative group of real number field

Published on 25 Mar 2026 - 6:24

score 964 · Answer 3 · 2026-03-25 17:26:52

964

Views

If $u\in F$ is Transcendental over $K$, $F$ an extension field of $K$, Show every element in $K(u)$ not in $K$ is transcendental over $K$.

Published on 25 Mar 2026 - 17:26

score 54 · Answer 4 · 2019-03-15 17:20:11

54

Views

Show that $n\in\mathbb{N}$ is square-free

Published on 15 Mar 2019 - 17:20

score 170 · Answer 5 · 2019-03-16 21:10:52

170

Views

Number of embeddings of a (nonsimple) extension of a field to another field

Published on 16 Mar 2019 - 21:10

score 204 · Answer 6 · 2026-03-25 09:34:30

204

Views

Prove if two normal extensions over a field are isomorphic

Published on 25 Mar 2026 - 9:34

score 46 · Answer 7 · 2019-03-17 09:10:56

46

Views

How to construct a given group as multiplicative group of field

Published on 17 Mar 2019 - 9:10

score 839 · Answer 8 · 2026-03-27 23:20:10

839

Views

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Published on 27 Mar 2026 - 23:20

score 91 · Answer 9 · 2026-03-30 22:16:52

Let $L/K$ be a field extension and let $a, b \in L$ be algebraic elements over $K$ having the same minimal polynomial. Show that $K(a) \simeq K(b)$.

score 316 · Answer 10 · 2019-03-18 00:18:17

316

Views

(Intermediate) normal extension is stable

Published on 18 Mar 2019 - 0:18

score 33 · Answer 11 · 2019-03-18 05:19:41

33

Views

Suppose $\zeta$ is a root of unity and $f\in \mathbb{Q}[X]$. Show that $f(\zeta)\neq2^{1/4}$.

Published on 18 Mar 2019 - 5:19

score 135 · Answer 12 · 2019-03-18 09:18:03

135

Views

Example of an infinite algebraic field extension which is not simple

Published on 18 Mar 2019 - 9:18

score 65 · Answer 13 · 2026-03-26 22:15:04

65

Views

First-order definability sums of squares

Published on 26 Mar 2026 - 22:15

score 61 · Answer 14 · 2026-04-01 10:30:50

61

Views

Let $K$ be an extension of a field $F$ such that $[K:F] = 13$.Suppose $a$ $∈$ $K-F$.What is the value of $[F(a):F] $?

Published on 01 Apr 2026 - 10:30

score 474 · Answer 15 · 2026-03-28 12:32:16

474

Views

Infinite perfect field of characteristic p

Published on 28 Mar 2026 - 12:32

List Question

Extension of Splitting Fields over An Arbitrary Field

Group automorphism of multiplicative group of real number field

If $u\in F$ is Transcendental over $K$, $F$ an extension field of $K$, Show every element in $K(u)$ not in $K$ is transcendental over $K$.

Show that $n\in\mathbb{N}$ is square-free

Number of embeddings of a (nonsimple) extension of a field to another field

Prove if two normal extensions over a field are isomorphic

How to construct a given group as multiplicative group of field

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Let $L/K$ be a field extension and let $a, b \in L$ be algebraic elements over $K$ having the same minimal polynomial. Show that $K(a) \simeq K(b)$.

(Intermediate) normal extension is stable

Suppose $\zeta$ is a root of unity and $f\in \mathbb{Q}[X]$. Show that $f(\zeta)\neq2^{1/4}$.

Example of an infinite algebraic field extension which is not simple

First-order definability sums of squares

Let $K$ be an extension of a field $F$ such that $[K:F] = 13$.Suppose $a$ $∈$ $K-F$.What is the value of $[F(a):F] $?

Infinite perfect field of characteristic p

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