Adapter coupled between a tire bead and a rim, and having an axially inner end mounted on the rim seat. The adapter comprises an inner reinforcer, an axially outer end that comprises an outer reinforcer, and a body that connects the outer and inner ends to form a single piece and comprises one main reinforcement that connects the outer and inner reinforcers. Substantially cylindrical adapter seat receives one of the tire beads, the seat being situated at the axially outer end of the body. An adapter bearing face is substantially contained in a plane perpendicular to the axis of rotation of the tire/rim rolling assembly, the bearing face being situated on the axially inner face of the axially outer end. The reinforcing element of the axially outer end is axially situated entirely on the outside of the bearing face. The body comprises, facing the adapter seat, an annular seat reinforcement.