2021/08/11 by Fernando Q. Gouvêa, Gouvêa, Fernando Q., Jonathan Webster +1
Mathematics · #01A55 #01A75 #11R04 #11R29 #Advanced Algebra and Geometry #FOS: Mathematics #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.2108.05327
openalex publication_date 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
The problem of the "common inessential discriminant divisors" attracted the attention of Dedekind, Kronecker, and Hensel in the early days of algebraic number theory. Four sources are particularly important: Dedekind's announcement, in 1871, of the second edition of Dirichlet's lectures \citeanzeige, Dedekind's 1878 paper, the 25th section of Kronecker's 1882 Grundzüge, and Hensel's 1894 paper, which is our focus here. Both of the key papers of Dedekind were translated and annotated in our paper "Dedekind on higher congruences and index divisors, 1871 and 1878." (arXiv:2107.08905. We here present an annotated translation of Kurt Hensel's "Arithmetische Untersuchungen über die gemeinsamen ausserwesentlichen Discriminantentheiler einer Gattung" (Journal für die Reine und Angewandte Mathematik, 113 (1894), 128--160).