2021/07/19 by Gouvêa, Fernando Q., Webster, Jonathan
#01A55 #01A75 #11R04 #11R29 #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2107.08905
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.