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arXiv · 2107.08905

Dedekind on Higher Congruences and Index Divisors, 1871 and 1878

Fernando Q. Gouvêa·Jonathan Webster
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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.

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Fernando Q. Gouvêa, Jonathan Webster. 2021-07-19. Dedekind on Higher Congruences and Index Divisors, 1871 and 1878. https://arxiv.org/abs/2107.08905

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