A Weil divisor on an integral normal variety is a finite formal linear
combination of integral subvarieties of codimension
one with integer coefficients. Each such subvariety is
called a prime divisor. A Weil divisor is effective
when every coefficient is nonnegative. Rational and
real Weil divisors allow coefficients in 
and 
,
respectively (Hartshorne 1977).
A nonzero rational function determines a principal Weil divisor by its orders of zeros and poles along prime divisors. Two Weil divisors are linearly equivalent when their difference is principal. A Cartier divisor determines a Weil divisor on a normal variety, but a Weil divisor need not be locally principal. On a smooth variety, every Weil divisor is a Cartier divisor.
