The general term for single-celled organisms with a nucleus is eukaryotes.

Here's why:

* Eukaryotes are organisms whose cells have a membrane-bound nucleus containing their genetic material (DNA).

* Prokaryotes, on the other hand, are single-celled organisms that lack a nucleus and other membrane-bound organelles.

So, while "single-celled" and "nucleus" are characteristics of eukaryotes, the most accurate term for them is eukaryotes.