The arithmetic of diophantine approximation groups I: linear theory

摘要

A paradigm for a global algebraic number theory of the realsis formulated with the purpose of providing a unified setting for algebraic and transcendental number theory. This is achieved through thestudy of subgroups of nonstandard models of Dedekind domains called diophantine approximation groups. The arithmetic of diophantine approximation groups is defined in a way which extends the ideal-theoretic arithmetic of algebraic number theory, using the structure of an approximate ideal: a bifiltration by subgroups along which partial products may be performed.