An electrical rotating machine includes a laminated stator core having a first axial duct to convey a cooling air stream generated by a turbomachine through the laminated stator core to a rear stator winding overhang, and a second axial duct to return the cooling air stream from the rear stator winding overhang back through the laminated stator core. An air guide is attached to the laminated stator core on a side of the rear stator winding overhang to redirect the cooling air stream via the rear stator winding overhang. Radial slots between the ducts and an air gap between the laminated stator core and a rotor are spaced from one another at an axial distance which decreases toward a turbomachine-distal side of the laminated stator core so as to compensate a temperature gradient caused by the one-sided cooling.