Steht es alles wirklich schon bei Dedekind? Ideals and Factorization between Dedekind and Noether

This article analyzes similarities and divergences between the approaches of Richard Dedekind and Emmy Noether to the problem of factorization in fields of algebraic numbers. Dedekind’s approach was highly idiosyncratic when seen in the context of late nineteenth-century algebra. In
many important senses it can be seen as the harbinger of the central ideas of
the structural approach to abstract algebra of which, beginning in the 1920s,
Emmy Noether and her school were the main promoters. Still, several decades
of intense mathematical research in the hands of important figures separate the
works of these two great masters. This raises the question that is addressed
in this article, namely, what are the differences between their approaches and
what was the process that led from that of the first to that of the second.