List questions from field-theory

Published on 14 Apr 2026 - 8:34

936

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non separable, non normal, finite field extension

Published on 28 Apr 2026 - 11:05

159

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

Published on 06 May 2026 - 7:34

155

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Extensions of maximally complete fields

Published on 29 Apr 2026 - 12:57

45

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

Published on 10 May 2026 - 12:32

42

Views

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

Published on 10 May 2026 - 12:39

147

Views

Is Homomorphism equivalent to Field extension?

Published on 29 Apr 2026 - 12:44

365

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

Published on 10 May 2026 - 11:42

208

Views

Finite separable extension, algebraically independent elements

Published on 14 Apr 2026 - 21:48

95

Views

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

Published on 29 Apr 2026 - 12:44

359

Views

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

Published on 09 Apr 2026 - 15:39

147

Views

Find the degree of the splitting field

Published on 13 Apr 2026 - 5:12

79

Views

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

Published on 15 Apr 2026 - 14:19

248

Views

Is a vector space with countable basis is countable?

Published on 26 Mar 2026 - 14:16

574

Views

Algebraic closure and field extension

Published on 14 Apr 2026 - 14:24

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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