Electric machine, - wherein the electric machine has a rotor which is arranged on a rotor shaft, - wherein the rotor shaft is supported in bearings such that the rotor together with the rotor shaft is rotatable around an axis of rotation, - wherein the rotor is surrounded radially on the outside by a stator and the stator radially on the outside by a casing, - wherein a first and a second covering element (8,9), which function as heat exchangers, are arranged at a first and a second axial end of the rotor and stator, by means of which the rotor and the stator are enclosed with respect to the environment of the electric machine, - wherein the first covering element is surrounded radially on the outside, and axially on the side facing away from the rotor and stator there, by an air guide element, and the second covering element is surrounded radially on the outside, and axially on the side facing away from the rotor and stator there, by an inner ring element, - wherein first and second cooling channels (14,21) running axially are arranged in the casing or between the casing and stator, and rotor channels running axially are arranged in the rotor shaft and/or in the rotor, - wherein the casing has an air inlet radially on the outside, via which a cooling air flow is fed to the first cooling channels, - wherein at least one part of the cooling air flow is fed via the first cooling channels to the air guide element or to an interspace between the first covering element and the air guide element, in other words to the first axial end of the machine, is deflected radially to the inside there, and is then fed via the rotor channels to the inner ring element or to an interspace between the second covering element and the inner ring element, is deflected radially to the outside there and fed to the second cooling channels, and is then routed by means of the second cooling channels axially through the electric machine, and finally escapes into the environment of the electric machine, and - wherein the inner ring element is surrounded radially on the outside at least over part of its periphery by an outer ring element, wherein third cooling channels running axially are arranged in the casing or between the casing and stator, wherein a further part of the cooling air flow is fed to the outer ring element or to an interspace between the casing and the outer ring element, in other words to the second axial end of the machine, is deflected tangentially there and fed to the third cooling channels, and is finally routed by means of the third cooling channels axially through the electric machine, and then escapes into the environment of the electric machine. - wherein the electric machine has a rotor which is arranged on a rotor shaft, - wherein the rotor shaft is supported in bearings such that the rotor together with the rotor shaft is rotatable around an axis of rotation, - wherein the rotor is surrounded radially on the outside by a stator and the stator radially on the outside by a casing, - wherein a first and a second covering element (8,9), which function as heat exchangers, are arranged at a first and a second axial end of the rotor and stator, by means of which the rotor and the stator are enclosed with respect to the environment of the electric machine, - wherein the first covering element is surrounded radially on the outside, and axially on the side facing away from the rotor and stator there, by an air guide element, and the second covering element is surrounded radially on the outside, and axially on the side facing away from the rotor and stator there, by an inner ring element, - wherein first and second cooling channels (14,21) running axially are arranged in the casing or between the casing and stator, and rotor channels running axially are arranged in the rotor shaft and/or in the rotor, - wherein the casing has an air inlet radially on the outside, via which a cooling air flow is fed to the first cooling channels, - wherein at least one part of the cooling air flow is fed via the first cooling channels to the air guide element or to an interspace between the first covering element and the air guide element, in other words to the first axial end of the machine, is deflected radially to the inside there, and is then fed via the rotor channels to the inner ring element or to an interspace between the second covering element and the inner ring element, is deflected radially to the outside there and fed to the second cooling channels, and is then routed by means of the second cooling channels axially through the electric machine, and finally escapes into the environment of the electric machine, and - wherein the inner ring element is surrounded radially on the outside at least over part of its periphery by an outer ring element, wherein third cooling channels running axially are arranged in the casing or between the casing and stator, wherein a further part of the cooling air flow is fed to the outer ring element or to an interspace between the casing and the outer ring element, in other words to the second axial end of the machine, is deflected tangentially there and fed to the third cooling channels, and is finally routed by means of the third cooling channels axially through the electric machine, and then escapes into the environment of the electric machine.