1945/01/01 by Emil Artin, G. Whaples · 2 citations
Mathematics · Computer Science · #Mathematical and Theoretical Analysis #Optimization and Variational Analysis #Characterization (materials science) #Mathematics #Axiom #Product (mathematics) #Geometry #Materials science #Nanotechnology
paper · pdf · doi:10.1090/s0002-9904-1945-08383-9
openalex publication_date 1945/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
Introduction. The theorems of class field theory are known to hold for two kinds of fields: algebraic extensions of the rational field and algebraic extensions of a field of functions of one variable over a field of constants. We shall refer to these fields as number fields and function fields, respectively. For class field theory, the function fields must indeed be restricted to those with a Galois field as field of constants; however, we make this restriction only in 5, and until then consider fields with an arbitrary field of constants.