Idelic modulus
= Idelic modulus
{title2=$\|x\|=\prod_v|x_v|_v$}
The idelic modulus is the product of normalized local moduli: ordinary real modulus, squared complex modulus and $(N\mathfrak p)^{-\operatorname{ord}_{\mathfrak p}(x)}$ at finite places. This continuous homomorphism to $\mathbb R_{>0}$ has the diagonal multiplicative group in its kernel by the <product formula>. It differs from the <idele norm>, which maps between idele groups of field extensions.