What is the type of cell that doesn't have a membrane around their nuclear material?

The type of cell that doesn't have a membrane surrounding their nuclear material is called a prokaryotic cell. Prokaryotes, which include bacteria and archaea, have a simpler cellular structure without a true nucleus; instead, their genetic material is located in a region called the nucleoid. This lack of a nuclear membrane distinguishes them from eukaryotic cells, which do have a defined nucleus encased in a membrane.