## Abstract

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.

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.

Original language | English |
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Title of host publication | In Memoriam Richard Dedekind (1831-1916) |

Subtitle of host publication | number theory, algebra, set theory, history, philosophy : Konferenzbeiträge aus Anlass des 100. Todestages, TU Braunschweig, 6.-8. Oktober 2016 |

Editors | Katrin Scheel, Th Sonar, Peter Ullrich |

Place of Publication | Münster |

Pages | 134-159 |

Number of pages | 26 |

ISBN (Electronic) | 9783959870443; 3959870442 |

State | Published - 2017 |

### Publication series

Name | Schriften zur Geschichte der Mathematik und ihrer Didaktik |
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Volume | 3 |