On the discovery of the analogy between number and function fields: The origin of Dedekind rings
type: Item
instance of: scholarly article
title: On the discovery of the analogy between number and function fields: The origin of Dedekind rings
zbMATH Open document ID: 0943.11002
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1999-11-14T00:00:00Z
review text: The deep analogy between number fields and function fields was a source of deep problems and great insights especially in the second half of the 20th century. In this paper, the author restricts his attention to function fields of one variable over the field of complex numbers, and he describes how this analogy was discovered by Kronecker, Weierstraß, Dedekind and Weber, how mathematicians reacted to the introduction of algebraic methods to the theory of functions, and how Emmi Noether eventually formulated the axioms for Dedekind rings in the 1920s. Reviewer's remark: The term ``Dedekind ring'', credited in this paper to I. S. Cohen in 1950, was already used by \textit{J. Dieudonné} in 1947 [see Ann. Sci. Éc. Norm. Supér. (3) 64, 101--117 (1947; Zbl 0033.24801)].
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 11Rxx
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 14-03
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 1346292
zbMATH Keywords: function fields
zbMATH Keywords: Kronecker
zbMATH Keywords: Dedekind
zbMATH Keywords: Weber
zbMATH Keywords: Hensel
zbMATH Keywords: Noether
zbMATH Keywords: Dedekind rings
author: Peter Ullrich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1346292