An element of an Adéle Group, sometimes called a Repartition in older literature. Adéles arise in both Number Fields and Function Fields. The adéles of a Number Field are the additive Subgroups of all elements in , where is the 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 Place of an element of such that there are only a finite number of Places for which .
See also Idele
References
Chevalley, C. C. Introduction to the Theory of Algebraic Functions of One Variable.
Providence, RI: Amer. Math. Soc., p. 25, 1951.
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.