The rotary electrical machine comprises, in front, a pulley (3) secured to a shaft (9) of a rotor (20) passing through the front bearing (1a) of a housing. The bearing includes a base, having a nose (18) for mounting a front ball bearing (7) for rotating the shaft (9), and air inlets (15) defined by arms belonging to an outwardly opening area connecting a peripheral strip of material from the base to the nose (18) in order to shift the nose (18) toward the front in accordance with the central body of a device (100) for adjusting the tension of a belt received in the groove (31) of the pulley (3) and attached onto the housing (1a, 1b). The adjustment device (100) comprises at least one idler (200, 201) for tensioning the belt and a central opening (102) enabling passage of air through the air inlets (15).