Solvable extensions of number fields ramified at only one prime are Ostrowski

TL;DR

This paper proves that certain solvable number field extensions ramified at a single prime are Ostrowski, and generalizes Hilbert Theorem 94 to cyclic extensions ramified at one prime, expanding understanding of ramification in number fields.

Contribution

It establishes conditions under which solvable extensions ramified at one prime are Ostrowski and extends Hilbert Theorem 94 to cyclic ramified extensions.

Findings

Solvable extensions under certain conditions are Ostrowski.

Generalization of Hilbert Theorem 94 to cyclic ramified extensions.

Provides new insights into ramification behavior in number fields.

Abstract

In this note, we show that, under a certain condition, solvable extensions of number fields ramifed at only one prime are Ostrowski. As a corollary, we deduce a generalization of Hilbert Theorem 94 to cyclic extensions ramifed at one prime.