A process is proposed for production of dimethyl ether (DME) from synthesis gas (SG), in which at least one feed stream formed from synthesis gas (SG) is subjected to at least one synthesis step, in which components present in the feed stream are at least in part converted to dimethyl ether (DME), wherein at least one crude product stream is obtained which contains at least dimethyl ether (DME) and the unreacted components of the feed stream. The feed stream contains at least hydrogen, carbon monoxide and carbon dioxide, and has a stoichiometric number of 2.0 to 5.0. The feed stream further contains 4 to 20 mol percent carbon dioxide, and the ratio of carbon dioxide to carbon monoxide in the feed stream is in a range from 0.5 to 4. The at least one synthesis step is carried out under isothermal conditions. A system for production of dimethyl ether (DME) from synthesis gas (SG) is likewise subject matter of the present invention.