List questions from field-theory

246

Views

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Published on 02 Apr 2026 - 2:14

454

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Can an algebraic extension of an uncountable field be of uncountable degree?

Published on 09 Apr 2026 - 1:52

127

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characteristic of a field>0

Published on 12 Apr 2026 - 6:10

309

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Existence of "simple" irreducible polynomial of degree 12 in a finite field

Published on 28 Mar 2026 - 0:49

74

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If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

Published on 17 Jun 2014 - 17:51

79

Views

Commutative ring can be homomorphically mapped onto field

Published on 17 Jun 2014 - 21:01

12.7k

Views

Proving that a polynomial is not solvable by radicals.

Published on 03 Apr 2026 - 21:23

99

Views

Integral domain (rings and fields)

Published on 25 Mar 2026 - 15:48

212

Views

Let $F$ be a field. If $F^*$ is a cyclic group, must $F$ be a finite field?

Published on 28 Mar 2026 - 14:00

119

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Rings of algebraic integers

Published on 18 Jun 2014 - 21:31

143

Views

Galois extension of two fields

Published on 11 Apr 2026 - 13:37

82

Views

Show that a sequence of fields exists

Published on 02 Apr 2026 - 2:05

170

Views

Completion of a metric space vs. field extension

Published on 02 Apr 2026 - 2:08

791

Views

A field is finite if and only if its multiplicative group is finitely generated.

Published on 26 Mar 2026 - 9:42

625

Views

Show that $\operatorname{End}_{\mathbb{Z}}(\mathbb{Q})$ is isomorphic to the field $\mathbb{Q}$

Published on 06 Apr 2026 - 1:41

List Question

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Can an algebraic extension of an uncountable field be of uncountable degree?

characteristic of a field>0

Existence of "simple" irreducible polynomial of degree 12 in a finite field

If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

Commutative ring can be homomorphically mapped onto field

Proving that a polynomial is not solvable by radicals.

Integral domain (rings and fields)

Let $F$ be a field. If $F^*$ is a cyclic group, must $F$ be a finite field?

Rings of algebraic integers

Galois extension of two fields

Show that a sequence of fields exists

Completion of a metric space vs. field extension

A field is finite if and only if its multiplicative group is finitely generated.

Show that $\operatorname{End}_{\mathbb{Z}}(\mathbb{Q})$ is isomorphic to the field $\mathbb{Q}$

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