Editing Adele ring (section)

==Related notions==

The group of units in the adele ring is called the '''idele group'''
:<math>I_K = \mathbf{A}_{K}^\times</math>.
The quotient of the ideles by the subgroup <math>K^\times \subseteq I_K</math> is called the '''idele class group'''
:<math>C_K\ =\ I_K/K^\times.</math>
The '''integral adeles''' are the subring
:<math>\mathbf{O}_K\ =\ \prod O_\nu \ \subseteq \ \mathbf{A}_K.</math>