Subfields of the adele ring
The author establishes a \(1\)-\(1\) correspondence between immediate extensions of a Dedekind Ring and subfields of its rings of adeles containing its field of fractions. It is also shown that for any countable Dedekind Ring \(R\), there is an immediate extension \(R \subseteq R_0\) which is a Principal Ideal Ring.\ Some interesting related problems are also discussed.\ Applications are given in the classical case of algebraic number fields.
scientific article; zbMATH DE number 6051455