Jamieson, Fausset and Brown on 1 Kings 21:8

8. So she wrote letters in Ahab's name, and sealed them with his seal--The seal-ring contained the name of the king and gave validity to the documents to which it was affixed (Es 8:8; Da 6:17). By allowing her the use of his signet-ring, Ahab passively consented to Jezebel's proceeding. Being written in the king's name, it had the character of a royal mandate.

sent the letters unto the elders and to the nobles that were in his city--They were the civic authorities of Jezreel, and would, in all likelihood, be the creatures and fit tools of Jezebel. It is evident that, though Ahab had recently been in Jezreel, when he made the offer to Naboth, both he and Jezebel were now in Samaria (1Ki 20:43).