A permanently excited electrical machine, with a stator and a rotor, wherein either the stator comprises a coil arrangement and the rotor is provided with permanent magnet elements, or the rotor comprises a coil arrangement and the stator is provided with permanent magnet elements, - the stator - is arranged spaced from the rotor under forming an air gap, - comprises several segments oriented towards the air gap with mutually adjacent central poles with a winding of the coil arrangement and two side poles towards the air gap; - a one- or multipiece non-magnetic rotor back captively carries several mutually adjacent, magnetic conductive magnetic flux poles in the radial direction, wherein - each magnetic flux pole - has a hollow prismatic shape with at least one cooling duct, wherein each cooling duct has first and second through-holes (22a', 22a") in both end face ends and is adapted for flow of a cooling fluid, and - in cross-section, has an approximately circular ring segment or trapezoidal shape, wherein its longer concentric or parallel, respectively, side faces the air gap, and - one permanent magnet element each is accommodated between two mutually adjacent magnetic flux poles, wherein each one permanent magnet element each - in cross-section, has an approximately circular ring segment or trapezoidal shape, and - whose shorter concentric or parallel, respectively, side faces the air gap, and whose two inclined sides are oriented towards the respective opposite inclined sides of the magnetic flux poles, wherein - each of the permanent magnet elements is magnetically oriented essentially tangentially and two mutually adjacent permanent magnet elements are magnetically opposed, and wherein each central pole and its respective concentric winding are thermally coupled with a cooling device. - the stator - is arranged spaced from the rotor under forming an air gap, - comprises several segments oriented towards the air gap with mutually adjacent central poles with a winding of the coil arrangement and two side poles towards the air gap; - is arranged spaced from the rotor under forming an air gap, - comprises several segments oriented towards the air gap with mutually adjacent central poles with a winding of the coil arrangement and two side poles towards the air gap; - a one- or multipiece non-magnetic rotor back captively carries several mutually adjacent, magnetic conductive magnetic flux poles in the radial direction, wherein - each magnetic flux pole - has a hollow prismatic shape with at least one cooling duct, wherein each cooling duct has first and second through-holes (22a', 22a") in both end face ends and is adapted for flow of a cooling fluid, and - in cross-section, has an approximately circular ring segment or trapezoidal shape, wherein its longer concentric or parallel, respectively, side faces the air gap, and - has a hollow prismatic shape with at least one cooling duct, wherein each cooling duct has first and second through-holes (22a', 22a") in both end face ends and is adapted for flow of a cooling fluid, and - in cross-section, has an approximately circular ring segment or trapezoidal shape, wherein its longer concentric or parallel, respectively, side faces the air gap, and - one permanent magnet element each is accommodated between two mutually adjacent magnetic flux poles, wherein each one permanent magnet element each - in cross-section, has an approximately circular ring segment or trapezoidal shape, and - whose shorter concentric or parallel, respectively, side faces the air gap, and whose two inclined sides are oriented towards the respective opposite inclined sides of the magnetic flux poles, wherein - in cross-section, has an approximately circular ring segment or trapezoidal shape, and - whose shorter concentric or parallel, respectively, side faces the air gap, and whose two inclined sides are oriented towards the respective opposite inclined sides of the magnetic flux poles, wherein - each of the permanent magnet elements is magnetically oriented essentially tangentially and two mutually adjacent permanent magnet elements are magnetically opposed, and wherein each central pole and its respective concentric winding are thermally coupled with a cooling device.