History is self correcting. I can see that they thought of your definition. Why call something an empire if you don;t want to have an emperor. By your definition they could have taken over China and still wouldn’t have been an empire.
After you cited all those scholars it was very easy to come up with an alternative explanation. And of course I cited different definitions.
Was the British Empire ruled by a king or by parliament and a prime minister? Did it have an emperor?
Is the science settled? LOL.
No, the science isn't settled, but what is absolutely settled is that August was the first Roman emperor, whether you agree, or not.
The ruler of the Persian Empire was a king, not an emperor.
Oops - Roosevelt didn’t use the word democracy. My apologies Teddy.