Dedekind on Higher Congruences and Index Divisors, 1871 and 1878
Number Theory
2021-07-20 v1 History and Overview
Abstract
Dedekind's theorem connecting ideal theory and polynomial congruences appears in all textbooks on algebraic number theory, but few books note its connection to the problem of ``common index divisors.'' As part of a project to study the history of this problem, we present an annotated translation of two of Dedekind's papers on the subject: a notice about the first publication of Dedekind's ideal theory in 1871 and a paper of 1878 giving proofs of the results announced in 1871 and giving a necessary and sufficient condition for the existence of common index divisors. A separate paper will analyze Hensel's 1894 paper containing the same theorem.
Keywords
Cite
@article{arxiv.2107.08905,
title = {Dedekind on Higher Congruences and Index Divisors, 1871 and 1878},
author = {Fernando Q. Gouvêa and Jonathan Webster},
journal= {arXiv preprint arXiv:2107.08905},
year = {2021}
}