Adele ring
COMMUTATIVE RING, WHOSE ELEMENTS (CALLED ADELES) ARE AN INFINITE TUPLE OF ELEMENTS FROM EACH COMPLETION OF A NUMBER FIELD, SUCH THAT A COFINITE NUMBER OF THEM LIE IN THE RING OF ALGEBRAIC INTEGERS; "ADELE" IS SHORT FOR "ADDITIVE IDEAL ELEMENT"
Adelic; Valuation vector; Principal idele; Principal idèle; Ring of adeles; Ring of finite adeles
In mathematics, the adele ring of a global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic number theory. It is the restricted product of all the completions of the global field, and is an example of a self-dual topological ring.