List questions from field-theory

Published on 04 Apr 2026 - 2:33

859

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A Fixed Field of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$

Published on 04 Apr 2026 - 2:29

10.5k

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Additive inverse in a field is unique

Published on 12 Apr 2026 - 9:58

188

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Projective special linear groups are co-hopfian?

Published on 12 Apr 2026 - 2:41

58

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Irreducibility in Galois/non Galois Extensions

Published on 11 Apr 2026 - 20:29

216

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Proving that a field $K$ can be generated by algebraically independent elements and an separable element

Published on 29 Jul 2014 - 12:23

131

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real closure of an archimedean field

Published on 10 Apr 2026 - 20:03

1.4k

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What is the potential function of the field $\left(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2}\right)$

Published on 28 Mar 2026 - 6:10

3.4k

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Are all fields vector spaces?

Published on 31 Jul 2014 - 19:49

486

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Milne's Galois Theory Example

Published on 12 Apr 2026 - 7:24

72

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Extensions of degree $1$.

Published on 10 Apr 2026 - 8:25

153

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Query on an example of Morandi's Field and Galois Theory, regarding the degree of a field extension.

Published on 29 Mar 2026 - 0:00

939

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Families of Polynomials Irreducible in $\mathbb{Z}$ but reducible in $\mathbb{Z}/p\mathbb{Z}$ for all primes $p$.

Published on 11 Apr 2026 - 7:26

112

Views

Sources about transcendence degree

Published on 09 Apr 2026 - 18:13

150

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Field of Definition of an Algebraic Group

Published on 10 Apr 2026 - 21:44

List Question

Galois group of the splitting field of $ x^6 - 5$

A Fixed Field of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$

Additive inverse in a field is unique

Projective special linear groups are co-hopfian?

Irreducibility in Galois/non Galois Extensions

Proving that a field $K$ can be generated by algebraically independent elements and an separable element

real closure of an archimedean field

What is the potential function of the field $\left(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2}\right)$

Are all fields vector spaces?

Milne's Galois Theory Example

Extensions of degree $1$.

Query on an example of Morandi's Field and Galois Theory, regarding the degree of a field extension.

Families of Polynomials Irreducible in $\mathbb{Z}$ but reducible in $\mathbb{Z}/p\mathbb{Z}$ for all primes $p$.

Sources about transcendence degree

Field of Definition of an Algebraic Group

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