Rotary electric machine having: - a stator, a rotor rotating inside the stator, a shaft secured to the rotor, the shaft having an axis of symmetry that constitutes the axis of rotation, and front and rear rolling bearings (7, 8) rotationally receiving the shaft, - a casing shaped so as to be fastened to a fixed part, in which casing the stator is mounted, said casing comprising a front bearing and a rear bearing (lb), - the machine also having, mounted at the front of and outside the casing, a pulley, provided with a groove and secured to the rotor shaft passing through the front bearing, said front bearing (la) comprising an end wall (238, 138, 28, 18) provided with a nose for mounting the front ball bearing and with air inlet openings delimited by arms (138, 28) connecting the nose to a peripheral strip of material of the end wall, - the machine also having a device for adjusting the tension of a belt for transmitting movement that engages the groove of the pulley, said device for adjusting the tension being fastened to the front bearing of the casing and having at least one roller (200, 201) for tensioning the belt and a central opening allowing air to pass through the air inlet openings, characterized in that - the arms (138, 28) belong to a zone that is flared towards the outside of the casing and connects the strip of material to the nose so as to shift the nose forwards, and in that - shifting the nose forwards, with respect to the strip of material, depends on the central thickness of the device for adjusting the tension of the belt and is realized such that the groove is radially aligned with the one or more rollers (200, 201) of the adjustment device. - a stator, a rotor rotating inside the stator, a shaft secured to the rotor, the shaft having an axis of symmetry that constitutes the axis of rotation, and front and rear rolling bearings (7, 8) rotationally receiving the shaft, - a casing shaped so as to be fastened to a fixed part, in which casing the stator is mounted, said casing comprising a front bearing and a rear bearing (lb), - the machine also having, mounted at the front of and outside the casing, a pulley, provided with a groove and secured to the rotor shaft passing through the front bearing, said front bearing (la) comprising an end wall (238, 138, 28, 18) provided with a nose for mounting the front ball bearing and with air inlet openings delimited by arms (138, 28) connecting the nose to a peripheral strip of material of the end wall, - the machine also having a device for adjusting the tension of a belt for transmitting movement that engages the groove of the pulley, said device for adjusting the tension being fastened to the front bearing of the casing and having at least one roller (200, 201) for tensioning the belt and a central opening allowing air to pass through the air inlet openings, characterized in that - the arms (138, 28) belong to a zone that is flared towards the outside of the casing and connects the strip of material to the nose so as to shift the nose forwards, and in that - shifting the nose forwards, with respect to the strip of material, depends on the central thickness of the device for adjusting the tension of the belt and is realized such that the groove is radially aligned with the one or more rollers (200, 201) of the adjustment device.