No, stove top burners should not be washed in a dishwasher. Stove top burners are typically made of metal, and exposing them to the high temperatures and water pressure in a dishwasher can cause damage to the burners or affect their performance.
It is best to clean stove top burners by hand using mild dish soap, warm water, and a soft cloth or sponge. You can remove the burners from the stove, if possible, and wash them separately. Gently scrub away any food residue or grease, and rinse them thoroughly. Make sure the burners are completely dry before reattaching them to the stove.
If you have specific cleaning instructions or recommendations provided by the manufacturer of your stove top burners, it is advisable to follow those instructions for the best results and to avoid any potential damage.