Adéle
An element of an Adéle Group, sometimes called a Repartition in older literature. Adélesarise in both Number Fields and Function Fields. The adéles of aNumber Field are the additive Subgroups of all elements in 
, where 
is thePlace, 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 everyPlace 
of an element 
of such that there are only a finite number ofPlaces for which 
.
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.
- Eisenstein Prime
- Eisenstein Series
- Eisenstein Unit
- Elastica
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- Elder's Theorem
- Election
- Electric Motor Curve
- Element
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- Elements
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