An adapter for a rolling assembly comprising a tire having two beads (B), a rim (J) with two rim seats (7), said adapter connecting one of the beads and the rim. The adapter has an axially inner end (10) comprising inner reinforcer element (16), and an axially outer end (15) comprising outer reinforcer element (15), respectively mounted on a rim seat (7). Body (11) connects said outer end (9) to said inner end (10). Main reinforcement connects said outer reinforcer (15), and said inner reinforcer (16), a substantially cylindrical adapter seat (18) receiving one of said beads (B), an adapter bearing face (21) substantially contained in a plane perpendicular to the rion otataxis. The reinforcer element (15) of the axially outer end (9) is entirely situated axially outside the bearing face (21), and in that the body (11) comprises, opposite the adapter seat (7), an annular seat reinforcer (19).