On the discovery of the analogy between number and function fields: The origin of Dedekind rings
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)].
scientific article; zbMATH DE number 1346292