A commutative ring is said to be normed if there exists a multiplicative function $N:R\to \mathbb{N}$ such that $N(x y)=N(x)N(y)$, $N(x)=0$ iff $x$ divides $0$ and $N(x)=1$ iff $x$ is a unit.
I am working on the following problem which require an understanding of this concept:
Verify that $\mathbb{Z}[\sqrt n]$ and $\mathbb{Z}[i\sqrt n]$ where $n\in \mathbb{N},n>1$ and $n$ is square-free in $\mathbb{Z}$ are normed.