Abstract: An electrical synchronous machine of the type with smooth poles and with a constant air gap, comprising a rotor (2) in which the coils are accommodated in notches (4) extending from the periphery of the rotor and which is provided with a device of axial and if need be radial ventilation channels (8) and (9) and wherein the notches (4) over a polar pitch are directed in parallel relation to the axis of the pole and their depth (a) is chosen so as to increase the cross-section of the central zone defined by the bottoms of the notches (4) and comprising axial ventilation channels (8).