The turbojet family of engines are usually used in military aircraft. The word turbo implies that an axial turbine is used in the engine to extract work from the high pressure hot grasses. This runs the compressor and the utilities(electric generators, hydraulic pumps, mechanical loads) . In the turbojet, a large portion of the thrust is produced by the nozzle at the exhaust.
Turbojet - schematic
Turbojet - actual
Simple fluid model
Ideal Cycle
The turbojet works by imparting a large momentum to a small mass of incoming air.
The propeller on the other hand imparts a smaller momentum to a large mass of air.
The analysis of the turbojet is easier through the simple fluid mechanics model.
Continuity
Momentum