Question: there is (are) eukaryotic domain(s)?
Answer: Eukaryotes belong to the domain Eukaryota or Eukarya; their name comes from the Greek εὖ (eu, "well" or "good") and κάρυον (karyon, "nut" or "kernel"). The domain Eukaryota makes up one of the domains of life in the three-domain system; the two other domains are Bacteria and Archaea (together known as prokaryotes).