Matthew Poole and continuators on 1 Kings 4:1

SO king Solomon was king over all Israel .

This is spoken with respect to his Successors, who were Kings onely over a part, and that the smallest part of it. Or, in reference to the times of Division and Rebellion under David; when part went after David, and part after Ishbosheth; or part after Absalom, or Zeba, or Adonijah: but now all Israel were united under Solomon, and adhered to him, not onely a part of them; especially since the death of Adonijah and Ioab (who may be suspected to have watched an opportunity of revolting), and the confinement of Abiathar, and of Shimei (if not his death also) who could now have little or no interest or opportunity of setting up a party against Solomon (their principals being taken away, to whom they were but accessaries); nor in probability, any design to attempt it.