Idele

The multiplicative subgroup of all elements in the product of the multiplicative groups $k_\nu^\times$ whose absolute value is 1 at all but finitely many $\nu$, where $k$ is a number Field and $\nu$ a Place.

See also Adéle

References

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.