Lorenzen's reshaping of Krull's Fundamentalsatz for integral domains (1938--1953)

TL;DR

This paper explores Lorenzen's reformulations of Krull's Fundamentalsatz for integral domains, highlighting the historical development and mathematical insights through analysis of his writings and correspondence.

Contribution

It provides a detailed historical and conceptual analysis of Lorenzen's modifications of Krull's Fundamentalsatz, emphasizing the evolution of his ideas from 1938 to 1953.

Findings

Lorenzen's reformulations offered new perspectives on the Fundamentalsatz.

The correspondence reveals the collaborative and developmental process behind these reformulations.

The study clarifies the conceptual shifts in Lorenzen's approach to integral domains.

Abstract

Krull's Fundamentalsatz, the generalisation of the main theorem of elementary number theory to integral domains, is the starting point of Lorenzen's career in mathematics. This article traces a conceptual history of Lorenzen's successive reformulations of the Fundamentalsatz on the basis of excerpts of his articles. An edition of the extant correspondence of Lorenzen with Hasse, Krull, and Aubert provides a better understanding of the context of these investigations.