No, archaea do not have a nucleus. Instead, their genetic material is located in a region called the nucleoid, which is not surrounded by a membrane.
This lack of a true nucleus is one of the distinguishing features that separates archaea from eukaryotes, organisms that do have a defined nucleus. Archaea are prokaryotic organisms, meaning they are generally simpler in structure than eukaryotes, which include plants, animals, fungi, and protists.
The lack of a nuclear membrane allows archaea to reproduce swiftly and efficiently, contributing to their ability to thrive in a variety of extreme environments, such as high-temperature hot springs and highly saline lakes. Understanding the structure of archaea helps scientists appreciate the diversity of life forms on Earth and the evolutionary relationships between different types of organisms.