Rotary electrical machine comprising at the front a pulley (3) which is provided with a groove (31), and is integral with a rotor (20) shaft (9) passing through the front bearing (1a) of a housing configured to be secured on a fixed part, the said bearing (1a) comprising a base (238, 138, 28, 18) provided with a nose (18) for fitting of a front ball bearing (7) for rotation of the shaft (9), and air inlet openings (15) delimited by arms (138, 28) which connect the nose (18) to a peripheral strip of material (238) of the base, wherein the arms (138, 28) belong to an area (138, 28) which widens towards the exterior, connecting the strip of material (238) to the nose (18) for offsetting of the nose (18) at the front, further comprising a device (100) for regulation of the tension of a belt, said belt being received in the groove (31) in the pulley (3), and said device being secured on the housing (1a, 1b), wherein the regulation device (100) comprises at least one roller (200, 201) for tensioning of the belt, and a central opening (102) which permits passage of the air through the air inlet openings (15), and wherein the offsetting of the nose (18) at the front relative to the strip of material (238) depends on the central thickness of the regulation device (100).