Electrical rotating machine, in particular an alternator for a motor vehicle, comprising a cooling device for producing a forced flow of a cooling fluid, such as air, in the axial direction of the machine, between cooling fins and comprising an arrangement for rectifying the current, the arrangement comprising: - a support device for a plurality of positive diodes which comprises two support portions for diodes, • each portion of the support generally being in the form of an elongate plate, which are aligned in the peripheral direction about the axis of the machine, • the support device being fixed to the rear bearing by three fixing locations (53, 54, 54', 84, 85), one of the three is located in the junction zone (54, 54', 84) of the two portions and in that the arrangement further comprises - a support for a plurality of negative diodes in the form of a plate which is part of the rear bearing of the machine, - a diode connector, and wherein: • the supports of the positive diodes and negative diodes and the connector are superimposed in the direction of the axis of the machine, • the support of the positive diodes forms a positive radiator (50, 51, 51') which carries, on the front frontal face which is orientated towards the axis of the machine, the cooling fins which extend, at one side, in the axial flow and, at the other side, in the radial direction of the machine, • the positive radiator device (50, 51, 51') is produced in the form of at least one moulded component (50, 51, 51'), of which the face orientated towards the above-mentioned axis carries cooling fins which produce a heat exchange surface. - a support device for a plurality of positive diodes which comprises two support portions for diodes, • each portion of the support generally being in the form of an elongate plate, which are aligned in the peripheral direction about the axis of the machine, • the support device being fixed to the rear bearing by three fixing locations (53, 54, 54', 84, 85), one of the three is located in the junction zone (54, 54', 84) of the two portions and in that the arrangement further comprises • each portion of the support generally being in the form of an elongate plate, which are aligned in the peripheral direction about the axis of the machine, • the support device being fixed to the rear bearing by three fixing locations (53, 54, 54', 84, 85), one of the three is located in the junction zone (54, 54', 84) of the two portions and in that the arrangement further comprises - a support for a plurality of negative diodes in the form of a plate which is part of the rear bearing of the machine, - a diode connector, and wherein: • the supports of the positive diodes and negative diodes and the connector are superimposed in the direction of the axis of the machine, • the support of the positive diodes forms a positive radiator (50, 51, 51') which carries, on the front frontal face which is orientated towards the axis of the machine, the cooling fins which extend, at one side, in the axial flow and, at the other side, in the radial direction of the machine, • the positive radiator device (50, 51, 51') is produced in the form of at least one moulded component (50, 51, 51'), of which the face orientated towards the above-mentioned axis carries cooling fins which produce a heat exchange surface. • the supports of the positive diodes and negative diodes and the connector are superimposed in the direction of the axis of the machine, • the support of the positive diodes forms a positive radiator (50, 51, 51') which carries, on the front frontal face which is orientated towards the axis of the machine, the cooling fins which extend, at one side, in the axial flow and, at the other side, in the radial direction of the machine, • the positive radiator device (50, 51, 51') is produced in the form of at least one moulded component (50, 51, 51'), of which the face orientated towards the above-mentioned axis carries cooling fins which produce a heat exchange surface.