Norm of a fractional ideal ($N_{L/K}(I)$)

For a fractional ideal $I$ of ${\mathcal{O}}_L$, the relative ideal norm is the fractional ideal of ${\mathcal{O}}_K$ obtained multiplicatively from prime-ideal norms. Equivalently, its local valuation is the determinant valuation of $I$ as an ${\mathcal{O}}_K$-lattice relative to ${\mathcal{O}}_L$.