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The problem of the "common inessential discriminant divisors" attracted theattention of Dedekind, Kronecker, and Hensel in the early days of algebraicnumber theory. Four sources are particularly important: Dedekind'sannouncement, in 1871, of the second edition of Dirichlet's lectures\cite{anzeige}, Dedekind's 1878 paper, the 25th section of Kronecker's 1882\textit{Grundz\"uge}, and Hensel's 1894 paper, which is our focus here. Both ofthe key papers of Dedekind were translated and annotated in our paper "Dedekindon higher congruences and index divisors, 1871 and 1878." (arXiv:2107.08905}.We here present an annotated translation of Kurt Hensel's "ArithmetischeUntersuchungen \"uber die gemeinsamen ausserwesentlichen Discriminantentheilereiner Gattung" (\textit{Journal f\"ur die Reine und Angewandte Mathematik},\textbf{113} (1894), 128--160).

Kurt Hensel on Common Inessential Discriminant Divisors, 1894