'Kingdom' in the Bible

Now in the first year of Cyrus king of Persia, that the word of the LORD by the mouth of Jeremiah might be fulfilled, the LORD stirred up the spirit of Cyrus king of Persia, that he made a proclamation throughout all his kingdom, and put it also in writing, saying,

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

Be diligent and take precautions so that you do not neglect your responsibility in this matter. Why should the kingdom sustain any more damage?

I issue a decree that any of the Israelites in my kingdom, including their priests and Levites, who want to go to Jerusalem, may go with you.

all that is by the decree of the God of heaven, let be done diligently for the house of the God of heaven; for why is there wrath against the kingdom of the king and his sons?