The present disclosure relates to a hard sealing ring, comprising an annular body which has a basic shape that is rotationally symmetrical with respect to an axis. In a cross-section lying in the direction of the axis, the annular body comprises a contact portion which is arranged on an end face of the annular body. The contact portion points outwards in the direction of the axis. In the cross-section, the annular body also comprises a trough portion, which is arranged on a radial lateral surface of the annular body and faces away from the contact portion in relation to the direction of the axis. On the contact portion, the annular body comprises an anti-friction coating which is in particular single- or multi-layered.