List questions from extension-field

Published on 25 Mar 2026 - 11:54

221

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Number of F-homomorphism from K to E

Published on 16 Jul 2020 - 8:58

420

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For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

Published on 29 Mar 2026 - 5:50

101

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Elementary field theory question

Published on 18 Jul 2020 - 3:00

85

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Confusion in Proof of Primitive element theorem

Published on 19 Jul 2020 - 14:33

861

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If Gal$(K/\mathbb{Q}) = S_5$ then $K$ is the splitting field of a degree $5$ polynomial

Published on 29 Mar 2026 - 5:43

315

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Let $f(x) \in \mathbb{Q}[x]$ be an irreducible polynomial of degree $4$ with exactly $2$ real roots.

Published on 29 Mar 2026 - 5:44

114

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degree of minimal polynomial and degree of field extension

Published on 22 Jul 2020 - 7:00

329

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If $F, K$ are fields, $F$ algebraically closed, and $F \subseteq K$ then $K = F$?

Published on 24 Jul 2020 - 17:24

118

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Is a field extension of the form $\mathbb C[X, Y]/\mathfrak m$ isomorphic to $\mathbb C(k)$ for some algebraic $k$?

Published on 24 Jul 2020 - 18:32

56

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An extension field induces new variety

Published on 24 Jul 2020 - 19:44

66

Views

A problem to show that a certain field extension is not normal

Published on 23 Feb 2026 - 1:03

108

Views

Extending isomorphism to compositum of fields

Published on 06 Jul 2016 - 7:24

2.2k

Views

Eigenvalues of matrices over finite fields

Published on 03 Apr 2026 - 1:05

409

Views

Field and ideal notation: double bracks/parens vs single brackets/parens

Published on 03 Apr 2026 - 0:58

List Question

In characteristic 2 the splitting field of a cubic has degree 6

Number of F-homomorphism from K to E

For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

Elementary field theory question

Confusion in Proof of Primitive element theorem

If Gal$(K/\mathbb{Q}) = S_5$ then $K$ is the splitting field of a degree $5$ polynomial

Let $f(x) \in \mathbb{Q}[x]$ be an irreducible polynomial of degree $4$ with exactly $2$ real roots.

degree of minimal polynomial and degree of field extension

If $F, K$ are fields, $F$ algebraically closed, and $F \subseteq K$ then $K = F$?

Is a field extension of the form $\mathbb C[X, Y]/\mathfrak m$ isomorphic to $\mathbb C(k)$ for some algebraic $k$?

An extension field induces new variety

A problem to show that a certain field extension is not normal

Extending isomorphism to compositum of fields

Eigenvalues of matrices over finite fields

Field and ideal notation: double bracks/parens vs single brackets/parens

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