A synchronous electric motor with permanent magnets (1, 11). The synchronous electric motor includes a wound stator (11) having axially extending stator teeth (13) formed in a frame (10), and a rotor (1) having a plurality of permanent magnets (3) extending axially in first recesses (4) of a cylinder head (2). A dimensional ratio of a first outer diameter (D1) of the rotor (1) to a second outer diameter (D2) of the stator (11) is pre-determined so that the motor provides optimum efficiency. The dimensional ratio is pre-determined in such a way that the stator losses by Joule effect are reduced to a minimum. The synchronous electric motor is employed in electric compressors for motor vehicles.