List questions from kummer-theory | MathQA

Let $K$ be a field of characteristic $0$ containing $n$-th root of unity. Then, why $K(a^{1/n})＝K(b^{1/n})$ is equivalent to $b∈a(K^×)^n$?

Published on 25 Mar 2026 - 16:40

$X^m-a$ and $X^m-b$ irreducible with same splitting field, prove relation between $a$ and $b$.

Published on 25 Mar 2026 - 16:44

When is the splitting field of $x^n-a$ abelian?

Published on 25 Mar 2026 - 16:40

Silverman Prop 1.6

Published on 30 Apr 2026 - 11:07

Difference in field extensions when the field has $p$ roots of unity versus $p^2$ roots of unity.

Published on 25 Mar 2026 - 16:39

Can Kummer theory - there exists some $\gamma$, $L=K(\gamma^{1/n})$ - really be applied to any abelian extension $L/K$ (in characteristic zero, say)?

Published on 25 Mar 2026 - 16:40

Understanding the Kummer extension of semi-abelian varieties

Published on 25 Mar 2026 - 16:40

Galois group of the largest kummerian field over $K$

Published on 25 Mar 2026 - 16:39

Solving second order ODE - Hermite polynomial and Kummer confluent hypergeometric function

Published on 25 Mar 2026 - 16:38