NOVELTY - The compressor (101) has a housing (1) including a compression mechanism for compressing and discharging sucked fluid. A silencing and cooling device (32) cools the fluid and mitigates pressure fluctuation. The housing includes a cylinder block (3) integrally formed to include a compression space (3-A1) that accommodates the compression mechanism. A communicating hole (3-D) provides communication between the compression space and a silencing and cooling space (31). The silencing and cooling space is formed in recessed shape and includes a bottom portion.    USE - Roots air compressor for generating discharge pulsations and for compressing and sending fluid to a fuel cell of a passenger electric vehicle. Can also be used as a screw compressor, centrifugal compressor and a supercharger.    ADVANTAGE - The compressor utilizes fins to increase heat transfer area between fluid flowing in flow paths. The compressor utilizes cooling pipes to improve mutual heat exchange efficiency. The compressor allows compressed air to be straightened, so that pressure fluctuation is mitigated, thus reducing discharge pulsations. The compressor allows the compressed air to be discharged outside the compressor from a discharge outlet in a state at which the discharge pulsations are reduced, so that noise generated by the discharge pulsations is reduced. The compressor utilizes a cylinder block portion to accommodate a rotor chamber and a silencing and cooling chamber, so that rigidity and strength of coupling portions are improved. The compressor utilizes an intercooler core to improve heat exchange efficiency of the discharged air by the fins that protrude into the flow paths in which the discharged air flows. The compressor utilizes an upper wall formed into shell shape, so that rigidity of the upper wall is improved, thus reducing radiation of sound from the wall.    DESCRIPTION OF DRAWING(S) - The drawing shows a cross-sectional view of a compressor.    Housing (1)    Cylinder block (3)    Compression space (3-A1)    Communicating hole (3-D)    Silencing and cooling space (31)    Silencing and cooling device (32)    Roots air compressor (101)