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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 are a locally compact group with the rational numbers 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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