List questions from field-theory

Published on 11 Apr 2026 - 13:32

44

Views

Finding an algebraic number $z \in \mathbb{C}$ with Galois group over $\mathbb{Q}(\sqrt{5})$ equal to $\mathbb{Z}/7\mathbb{Z}$

Published on 12 Apr 2026 - 3:26

70

Views

Finding a counter-example for Gaussian-periods for non-primes

Published on 27 Mar 2026 - 21:05

702

Views

Are normal subgroups of finite index in an absolute Galois groups open?

Published on 20 Apr 2026 - 16:59

150

Views

Is this proof that $0x = 0$ correct?

Published on 25 Apr 2026 - 16:11

81

Views

Show that these elements are linearly independent

Published on 15 Apr 2026 - 10:57

595

Views

Can $\cos(2\pi/17)$ be written as nested square roots only?

Published on 13 Apr 2026 - 3:19

89

Views

Proof Kronecker Theorem: Help with Elementary Symmetric Functions

Published on 13 Apr 2026 - 13:15

46

Views

Square values of a polynomial

Published on 11 Apr 2026 - 8:49

88

Views

In a given field $F$, if $ab=0$, is it true that at least $a$ or $b$ has to be zero?

Published on 13 Apr 2026 - 20:59

63

Views

Justify adjoining roots of unity to solve a polynomial by radicals

Published on 13 Apr 2026 - 1:25

233

Views

Subset of $M_2(\mathbb{R})$ isomorphic to a field?

Published on 15 Apr 2026 - 13:40

113

Views

The roots of an irreducible polynomial over $\Bbb Z_p$ and a useful equivalence

Published on 15 Apr 2026 - 12:36

119

Views

If $K = F(\alpha)$ is a non separable and finite extension, then $T^K_F = 0$

Published on 09 Apr 2026 - 13:38

50

Views

Polynomials of degree $n$ with $\Bbb{F}_p$ are always reducible in $\Bbb{F}_{p^n}$

Published on 17 Apr 2026 - 0:26

List Question

Finite extensions

Finding an algebraic number $z \in \mathbb{C}$ with Galois group over $\mathbb{Q}(\sqrt{5})$ equal to $\mathbb{Z}/7\mathbb{Z}$

Finding a counter-example for Gaussian-periods for non-primes

Are normal subgroups of finite index in an absolute Galois groups open?

Is this proof that $0x = 0$ correct?

Show that these elements are linearly independent

Can $\cos(2\pi/17)$ be written as nested square roots only?

Proof Kronecker Theorem: Help with Elementary Symmetric Functions

Square values of a polynomial

In a given field $F$, if $ab=0$, is it true that at least $a$ or $b$ has to be zero?

Justify adjoining roots of unity to solve a polynomial by radicals

Subset of $M_2(\mathbb{R})$ isomorphic to a field?

The roots of an irreducible polynomial over $\Bbb Z_p$ and a useful equivalence

If $K = F(\alpha)$ is a non separable and finite extension, then $T^K_F = 0$

Polynomials of degree $n$ with $\Bbb{F}_p$ are always reducible in $\Bbb{F}_{p^n}$

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