i) The usual definition is more general, the coefficients of S can be taken in an arbitrary algebraic number field
presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field
, point set topological spaces, and classical noncommutative localization.
of Tokyo) explore similarities between algebraic number fields
and algebraic function fields in one variable over finite fields, explain adele rings and idele groups, derive several prime number theorems, and prove the main theorem of class field theory.