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Encyclopedia > Adele ring

  Results from FactBites:
 
Adele ring - Wikipedia, the free encyclopedia (491 words)
The use of adele rings in connection with Fourier transforms was exploited in Tate's thesis.
One key property of the additive group of adeles is that it is isomorphic to its Pontryagin dual.
The ring A is much used in advanced parts of number theory, often as the coefficients in matrix groups: that is, combined with the theory of algebraic groups to construct adelic algebraic groups.
Adele ring (335 words)
In number theory, the adele ring is a topological construction applied to the field of rational numbers (or, more generally, to an algebraic number field).
Topologically, the adeles A are a locally compact group with the rational numbers Q contained as a discrete subgroup.
The ring A is much used in advanced parts of number theory, often as the coefficients in matrix groups: that is, combined with the theory of algebraic groups.
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