Abstract: An electric machine has a stator and a rotor arranged on a hollow shaft and able to turn relative to the stator about an axis of rotation, wherein the hollow shaft comprises, in a shaft casing, at least one shaft exit opening for coolant supplied to a shaft interior space of the hollow shaft. A cover element is arranged next to the rotor on the hollow shaft, in which is formed a fluid duct comprising a fluid duct inlet and a fluid duct outlet, wherein the fluid duct inlet overlaps with the shaft exit opening and the fluid duct outlet overlaps with a coolant duct inlet of a coolant duct reaching through the rotor in the axial direction relative to the axis of rotation, having a coolant duct outlet on its side opposite the coolant duct inlet, through which the coolant emerges from the rotor.