On the degree of repeated radical extensions

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 $m_i$.