Q-Cartier divisor ($mD\text{ is Cartier for some }m\ge 1$)

A Weil divisor is Q-Cartier if some positive integer multiple is a Cartier divisor. Its Cartier index is the smallest such integer. It is ample in the Q-Cartier sense when such a multiple is an ample Cartier divisor. This need not make the original divisor itself Cartier.