List questions from galois-theory

Published on 29 Apr 2020 - 3:34

49

Views

Let $u$ be transcendental over $\mathbb{Z}_p$. Why is $t^p-u$ irreducible over $\mathbb{Z}_p(u)$?

Published on 29 Apr 2020 - 4:05

998

Views

Galois group of tamely ramified extension

Published on 25 Mar 2026 - 18:57

294

Views

Galois Groups and intermediate field extensions

Published on 04 Apr 2026 - 17:12

95

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Roots and Fixed Points

Published on 04 Apr 2026 - 17:07

42

Views

Bewersdorff Exercise problem: factorise a degree 6 reducible (over Q) polynomial

Published on 30 Mar 2026 - 5:16

53

Views

Asking for confirmation on my understanding of Galois theory

Published on 04 Apr 2026 - 17:12

110

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Roots of an irreducible polynomial in an extension field

Published on 02 Apr 2026 - 3:16

149

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Galois theory: Gal(K/F) divides [K:F]?

Published on 29 Apr 2020 - 22:34

51

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$f$ has double roots, but the field automorphism permutes the roots anyways

Published on 30 Apr 2020 - 8:10

29

Views

If $\mu_{p}(k)={1}$, $p$ is a prime, is the polynomial $\sum_{j=0}^{p-1}x^{j}$ irreducible over $k$?

Published on 27 Mar 2026 - 19:10

98

Views

Why $\mathbb{Q}(x_1,y_1,...,x_n,y_n)/\mathbb{Q}$ is a Galois extension? where $E[m]=\{(x_1,y_1),...,(x_n,y_n)\}$ is the m-torsion group.

Published on 25 Mar 2026 - 7:45

78

Views

Subgroup inavariant subextension of Galois extension

Published on 28 Mar 2026 - 16:14

192

Views

A Question on Stabilizers

Published on 28 Mar 2026 - 16:12

110

Views

In profinite group $G$ with inverse system $(G_\alpha)%$, how the kernel of projection map becomes the basis of neighborhood for $1$ in $G$?

Published on 25 Mar 2026 - 9:29

List Question

How exactly does a Galois group behave?

Let $u$ be transcendental over $\mathbb{Z}_p$. Why is $t^p-u$ irreducible over $\mathbb{Z}_p(u)$?

Galois group of tamely ramified extension

Galois Groups and intermediate field extensions

Roots and Fixed Points

Bewersdorff Exercise problem: factorise a degree 6 reducible (over Q) polynomial

Asking for confirmation on my understanding of Galois theory

Roots of an irreducible polynomial in an extension field

Galois theory: Gal(K/F) divides [K:F]?

$f$ has double roots, but the field automorphism permutes the roots anyways

If $\mu_{p}(k)={1}$, $p$ is a prime, is the polynomial $\sum_{j=0}^{p-1}x^{j}$ irreducible over $k$?

Why $\mathbb{Q}(x_1,y_1,...,x_n,y_n)/\mathbb{Q}$ is a Galois extension? where $E[m]=\{(x_1,y_1),...,(x_n,y_n)\}$ is the m-torsion group.

Subgroup inavariant subextension of Galois extension

A Question on Stabilizers

In profinite group $G$ with inverse system $(G_\alpha)%$, how the kernel of projection map becomes the basis of neighborhood for $1$ in $G$?

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