Who are the four emperors of heaven?

There are several sayings about the Four Emperors, and there are two common ones:

The school that advocates the greatest Three Qing Dynasties lists the Four Emperors as: the Jade Emperor of Zhongtian, the Purple Emperor of Arctic, the Emperor of Taiji Gouchen, and the Mother of the Earth. About the Jade Emperor in charge of the official department and the punishments department, Wei Zi in charge of the rites department and the fact department, Gou Chen in charge of the Ministry of War, and Hou Di in charge of the Ministry of Industry.

Those who advocate the largest jade emperor in heaven separate the jade emperor from the four emperors, and the influence of this division is not as great as the former. Their four emperors were: the Emperor Wei Zi in the Arctic, the immortal emperor in the Antarctic (the Jade Qing King in the early Yuan Dynasty, the ninth son or eldest son of the Buddha), the Qing Emperor in the East Pole (the Buddha who helped Taiyi), and the Emperor Xi in the West Pole (or Houdi, or others).