I should explain my question in detail as of now I'm sure it makes no sense.
Let $K$ be a global field (in particular I care about the characteristic $p$ case.)
Then its Idele group $I_K$ has a homormorphism into $\mathbb{R}_+$ defined by the map $a \mapsto\prod_P q_P^{-v_P(a)}$ and this is called the idelic norm. This map has a kernel say $I_K^0$.
For $K\subset L$ there is a natural norm map $N_{L/K}:I_L\rightarrow I_K$.
I want to know whether $N_{L/K}I_L^0\subset I_K^0$. I tried to do some calculation using some facts I know and I have not been able to attain a conclusion yet.