An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles
arise in both number fields and function
fields. The adèles of a number field are
the additive subgroups of all elements in 
, where 
is the field place, whose
absolute value is 
at all but finitely many 
s.
Let 
be a function
field of algebraic functions of one variable. Then a map 
which assigns to every field
place 
of 
an element 
of 
such that there are only a finite number of field places 
for which 
is called an adèle (Chevalley 1951, p. 1951).
