A pipe element is formed of a metal pipe and at least one metal connector, fastened to an end of the metal pipe such that torques and axial forces can be transmitted between the metal pipe and the metal connector. The metal connector has thread, in particular a conical thread, or a flange, by way of which the metal connector can be screwed to another metal connector of an additional pipe element in order to connect two pipe elements. The metal connector is screwed to an inner sleeve by way of a cylindrical thread so that the metal pipe is a really clamped between the metal connector on the outside and the inner sleeve on the inside in a connection region. The connection region is conically tapered toward the pipe end.