Correct! At the late part of the empire, one state was divided into two main imperial divisions, Eastern Roman and Western Roman (the latter fell in 476 AD, the latter in 1453 AD), and each of those was divided into two parts, so that there were 4 emperors as a whole. This was called a Tetrarchy, from the Greek word "tetra", meaning "four."
To make matters more confusing, each of the four divisions had three dioceses, making for 12 in all. Underneath all of THAT were the provinces, whose numbers Diocletian had increased to something like 100. Altogether, it was a complex, archaic, confusing, and ultimately doomed system which attempted to keep the warlords who effectively ran the empire together, keeping it in "one" piece for another couple of centuries. If there was anything "good" about this arrangement, it is that it gave Europe the concept of vassalage, which, while not a good thing in itself, did provide a foundation for at least some expected order, even when proper government failed.
Your turn, Saft.