History of the Roman Empire
Theodosius was the last Emperor who ruled over the whole Empire. After his death in 395, he gave the two halves of the Empire to his two sons Arcadius and Honorius; Arcadius became ruler in the East, with his capital in Constantinople, and Honorius became ruler in the West, with his capital in Milan and later Ravenna. The Roman state would continue to have two different emperors with different seats of power throughout the 5th century, though the Eastern Romans considered themselves to be the only ones who were fully Roman. Latin was used in official writings as much as, if not more than, Greek and the two halves were nominally, culturally and historically, if not politically, the same state.
Emperor
Historians generally refer to the continuing Roman Empire in the east as the Byzantine Empire after Byzantium, the original name of the town that Constantine I would elevate to the Imperial capital as New Rome in AD 330. (The city is more commonly called Constantinople and is today named Istanbul). Although the empire was again subdivided and a co-emperor sent to Italy at the end of the fourth century, the office became unitary again only 95 years later at the request of the Roman Senate and following the death of Julius Nepos, last Western Emperor. This change was a recognition of the reality that little remained of Imperial authority in the areas that had been the Western Empire, with even Rome and Italy itself now ruled by the essentially autonomous Odoacer.