On the degree of repeated radical extensions

TL;DR

This paper provides necessary and sufficient conditions for the degree of repeated radical extensions over an arbitrary field, answering a question posed by Mordell in 1953.

Contribution

It establishes a complete characterization of the degree of repeated radical extensions, extending Mordell's question from 1953.

Findings

Derived conditions for the degree of radical extensions

Solved Mordell's 1953 question in this context

Generalized previous results to arbitrary fields

Abstract

We answer a question posed by Mordell in 1953, in the case repeated radical extensions, and find necessary and sufficient conditions for $[F[\sqrt[m_1]{N_1},\dots,\sqrt[m_\ell]{N_\ell}]:F]=m_1\cdots m_\ell$, where $F$ is an arbitrary field of characteristic not dividing any $m_i$.