An adapter for a rolling assembly having a rotation axis and comprising a tire having two beads, a rim, said adapter having an axially inner end to be mounted on the rim seat and comprises an inner reinforcer element, an axially outer end to be mounted on the rim seat and comprises an outer reinforcer element, a body that connects said outer end to said inner end so as to form a single piece and comprises a main reinforcement connecting said outer reinforcer and said inner reinforcer, a substantially cylindrical adapter seat receiving one of said beads, an adapter bearing face substantially contained in a plane perpendicular to the rotation axis. The reinforcer of the axially outer end is entirely outside the bearing face, and the body comprises, opposite the adapter seat, an annular seat reinforcer having a compression modulus greater than or equal to 1 GPa.