The rotary electrical machine having a homopolar structure includes a number Npe of electrical phases. The machine includes a juxtaposition, along the rotational axis of the rotary electrical machine, of at least one pair of armatures having a number of poles Np, placed on both sides of at least one inductive coil wound around the rotational axis, two adjacent armatures being angularly offset by any electrical angle θs, preferably between 0° and 180°/Npe, and at least one “passive” inductor of ferromagnetic material, separated from the armatures by an air gap. Either the armatures form the rotor, or the inductor and the other element form the stator.