The method relates to processing by a separation technique of a gas mixture (k) that is formed from a product stream (d) of a reactor (4) for synthesizing dimethyl ether from synthesis gas (b), and which contains at least dimethyl ether, carbon dioxide, and at least one additional component having a lower boiling point than carbon dioxide. The gas mixture (k) is cooled down at a first pressure level from a first temperature level to a second temperature level, and a residual portion of the gas mixture (k) remaining gaseous at the second temperature level is washed in an absorption column (18) by a return flow (v) containing mainly carbon dioxide. The mainly carbon dioxide containing return flow (v) is at least partially formed from a portion of the gas mixture (k) which was separated as a liquid during the cooling process.
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