A Cartier divisor is said to be principal if it is in the image of the homomorphism formula_64 that is, if it is the divisor of a rational function on "X". Two Cartier divisors are linearly equivalent if their difference is principal. Every line bundle "L" on "X" on an integral Noetherian scheme is the class of some Cartier divisor. As a result, the exact sequence above identifies the Picard group of line bundles on an integral Noetherian scheme "X" with the group of Cartier divisors modulo linear equivalence. This holds more generally for reduced Noetherian schemes, or for quasi-projective schemes over a Noetherian ring, but it can fail in general (even for proper schemes over C), which lessens the interest of Cartier divisors in full generality.