what's in a name?

funny but this equation refer to the ring of (rational) adeles; which explains why i'm always levelheaded :).
According to the number theory, the adele ring is a topological ring ( occurs in mathematical analysis, for examples as rings of continuous real-valued functions on some topological space , where the topology is given by pointwise convergence), containing the field of rational numbers (or, more generally, to an algebraic number field). It involves all the completions of the field.
The word "adele" is short for "additive idele", and is also a French girl's name. Adeles were called valuation vectors or repartitions before about 1950.