A rotary electric machine having at least one piece of electric equipment constituted by an overmolded or jacketed electric motor or by an overmolded or jacketed magnetic suspension system; the electric equipment including firstly a rotor (102) and secondly a stator (150) having pole pieces (154) and coils (152); the stator (150) being provided with at least one jacket (101) or coating (190) to protect it against an aggressive environment, on its face situated facing the rotor (102); the protective jacket (101) or coating (190) on the face of the stator (150) facing the rotor (102) presenting set-back portions (111) set back from the main surfaces (155) defining the airgap (e), these set-back portions (111) being distributed around the stator; and the movement of fluid circulating in the airgap around the rotor (102) being thus enhanced.