= Principal Weil divisor
{title2=$\operatorname{div}(f)=\sum_D\operatorname{ord}_D(f)D$}
On a normal integral Noetherian scheme, a nonzero rational function defines the displayed <Weil divisor>, with the sum over codimension-one prime divisors. The <local ring> at each such divisor is a <discrete valuation ring>, so the order is well defined. The <divisor class group> is the group of <Weil divisors> modulo principal Weil divisors. On a smooth curve this agrees with a <principal divisor on an algebraic curve>.
Back to article page
