Charlemagne and the Byzantine Emperors ruled countries with the same name, Empire of the Roman People. Since the Byzantines got the name first, they were a bit upset when Charlemagne took it.
Please see the related question below for more information.
Justinian I
The two emperors who tried to restore order in the Roman Empire were Diocletian and Constantine I (or the Great).
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It was to expensive to restore the old Roman Empire
Justinian and Charlemagne were both influential rulers in medieval Europe who sought to consolidate and expand their empires. Justinian, as the Byzantine Emperor, is known for his legal reforms and the codification of Roman law, while Charlemagne, King of the Franks and later Emperor of the Carolingian Empire, is celebrated for his efforts to unite much of Western Europe and promote education and Christianity. Both leaders aimed to revive and preserve the legacy of the Roman Empire, albeit in different contexts. Their reigns significantly shaped the political and cultural landscapes of their respective territories.
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Byzantium
Constantinople was the capital of the Byzantine Empire, which had a long line of emperors from its founding in 330 AD until the fall of the city in 1453. There were a total of 88 Byzantine emperors, including co-emperors. The city was also the capital of the Eastern Roman Empire, which is often considered synonymous with the Byzantine Empire.
Byzantine art was paid for mostly by emperors and the Orthodox church.
Both emperors improved the Byzantine legal system by organizing laws more clearly.
they both had governed emperors
Justinian I
Diocletian
The Emperors Justinian and Basil II
Yes.
It varied. The Byzantine emperors reigned for life. Some of the emperors reigned for along time, while others died shorty after their accession to power. The length of the reign of emperors also depended on the political stability of he empire. The empire went thought periods of instability which was usurper emperors and/or civil wars. In such periods power changed hands quickly.
Yes and No. Comparing Byzantine emperors with Charlemagne in the time of 800 to 814 is comparing them with the one person who was probably the most powerful monarch of the Middle Ages. Later Byzantine emperors would have to be compared with western emperors of the Holy Roman Empire of their own times. Most of the emperors of the Holy Roman Empire were rather weak. This was partly because they were elected, and so there was no father to prepare the throne for them, but it was mostly because they had powerful feudal vassals, including kings, who limited their authority. Of course the Byzantine Empire gradually declined through the entire Middle Ages, leaving a rather decrepit country in the end, and an emperor of this country had no more power than his country did, and the Holy Roman Emperor had much more power than the Byzantine Emperor.