'Kingdom' in the Bible

These are the people of the divisions of the kingdom, among those who had been made prisoners by Nebuchadnezzar, the king of Babylon, and taken away by him, who went back to Jerusalem and Judah, every one to his town;

For they have not served thee in their kingdom, and in thy great goodness that thou gavest them, and in the large and fat land which thou gavest before them, neither turned they from their wicked works.

The Levites, in the days of Eliashib, Joiada, and Johanan, and Jaddua, are written, heads of fathers, and of the priests, in the kingdom of Darius the Persian.

Did not Solomon king of Israel sin [greatly against God] regarding these things? Yet among the many nations there was no king like him. He was loved by his God, and God made him king over all Israel; nevertheless the foreign women caused even him to sin [by turning to other gods and so, judged by God, he lost his kingdom].