Domestic electrical appliance, in particular a dishwashing machine

A domestic electrical appliance comprising:

• a main appliance body having a product treatment chamber;
• a door for closing an access opening to the product treatment chamber;
• and
• a locking device having a locking assembly arranged on one of two appliance components, the appliance components being the main appliance body and the door, and having a closing body arranged on the other of the two appliance components, wherein the locking assembly comprises a latch which is arranged to be movable between a release position and a latching position, which latch, in the latching position, engages behind the closing body in order to hold the door closed and, in the release position, releases the closing body to open the door,
• wherein there is formed on the locking assembly an aligning system for the mutual alignment of the closing body and the latch, which aligning system cooperates with the closing body as the door closes,
• wherein the latch and the aligning system are combined in a lock module which is mounted with play movability relative to a lock housing of the locking assembly.