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).
, where 
is the field place, whose absolute value is 
at all but finitely many 
s. 
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).