Yes, "hoi" means "the" in Greek, but the first 5 citations in the OED, and the most famous use of this phrase in English (in Gilbert and Sullivan's operetta _Iolanthe_), put "the" in front of "hoi". This is not a unique case: words "alchemy", "alcohol", "algebra", "alligator", and "lacrosse" incorporate articles from other languages, but can still be prefixed in English with "the". "The El Alamein battle" (which occurred in Egypt during World War II), sometimes proffered as a phrase with three articles, actually contains only two: _alamein_ is Arabic for "two flags" (which is appropriate for a town on the border between Egypt and Libya), and does not contain the Arabic article _al_. [from alt.english.usage FAQ]

>we don't normally say "the algebra" or "the alcohol"

maybe not as nouns but:
the algebra test was hard
the alcohol content would have killed a smaller man
the El Alamein defenses were flawed