List questions from field-theory

Published on 24 Mar 2026 - 23:43

931

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non separable, non normal, finite field extension

Published on 19 Mar 2026 - 23:54

150

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Given a local field $K$ how does one obtain the maximal unramified extension of $K$?

Published on 19 Mar 2026 - 23:42

150

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Extensions of maximally complete fields

Published on 26 Mar 2026 - 3:40

42

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Constructing a vector space of dimension $2$ for a cyclotomic field

Published on 24 Mar 2026 - 23:44

39

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How to show that there are no roots of $x^{q+1}+1$ in a finite field of size $q$

Published on 25 Mar 2026 - 7:46

141

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Is Homomorphism equivalent to Field extension?

Published on 22 Mar 2026 - 5:45

360

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The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

Published on 25 Mar 2026 - 1:17

205

Views

Finite separable extension, algebraically independent elements

Published on 31 Jan 2018 - 21:50

89

Views

Is $\mathbb R[x]/(x^2-2)=\mathbb R$?

Published on 25 Mar 2026 - 18:26

357

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How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

Published on 24 Mar 2026 - 22:13

143

Views

Find the degree of the splitting field

Published on 01 Feb 2018 - 13:21

76

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Let $F$ be a field. Show that if $x, y, z \in F $ and $x+z = y+z$ then $x = y.$

Published on 01 Feb 2018 - 16:50

247

Views

Is a vector space with countable basis is countable?

Published on 22 Mar 2026 - 10:09

571

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Algebraic closure and field extension

Published on 02 Feb 2018 - 6:27

List Question

Simple question on field extensions of separably closed fields

non separable, non normal, finite field extension

Given a local field $K$ how does one obtain the maximal unramified extension of $K$?

Extensions of maximally complete fields

Constructing a vector space of dimension $2$ for a cyclotomic field

How to show that there are no roots of $x^{q+1}+1$ in a finite field of size $q$

Is Homomorphism equivalent to Field extension?

The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

Finite separable extension, algebraically independent elements

Is $\mathbb R[x]/(x^2-2)=\mathbb R$?

How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

Find the degree of the splitting field

Let $F$ be a field. Show that if $x, y, z \in F $ and $x+z = y+z$ then $x = y.$

Is a vector space with countable basis is countable?

Algebraic closure and field extension

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