To provide a permanent magnet synchronous machine capable of expanding a high-speed operation range without reducing torque, and a pressing machine or an extrusion machine using the permanent magnet synchronous machine. In order to achieve the object described above, the present invention provides a permanent magnet synchronous electric machine having at least one permanent magnet on a radial surface of a rotor core, the permanent magnet having a rotor constituting a field pole, wherein a plurality of slits constituted by nonmagnetic material is provided on a core part between adjacent permanent magnets with opposite magnetic polarities of the rotor. According to the present invention, expansion of a high-speed operation range can be achieved without reducing torque.