A cell that does not have a nuclear membrane surrounding its DNA is called a prokaryote.

Here's why:

* Prokaryotes are single-celled organisms that lack a nucleus and other membrane-bound organelles. Their DNA is located in a region called the nucleoid, which is not enclosed by a membrane.

* Eukaryotes, on the other hand, have a true nucleus where their DNA is contained within a nuclear membrane.

Examples of prokaryotes include bacteria and archaea.